Finite Group Databasebeta

← Group #13169444

Character table — Group #13169444

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222224444444444444444448888888888888812121212121218181818181824242424242424242424242424242424242424242424242436363636363636363636363636363654545454
order122233344666666666333666666666121212121212366612121212121212121212444444444444121212121212121212121212121212121212121212121212224666612121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-1111111-1-11111-1-1-1-111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-11111
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-1111111-1-111-1-1-1-111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-11-11111111-11-111-1-11-11-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-1-1111-1-1-1-11-11-1-1-1111-11-111-1-111-1-1-1-11111-11111-1-1-1-1-1-111-1-111
χ111111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-111-1-11-1-1111-1-11-1-1111-1-1-1-11111-1-1-111-1-1111111-1-1-1-1-1-111
χ121111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-11-1-1-1-1111-1-11-1-1111-1-1111-1-1-1-111-1-1111-1111-1-111-1-111-1-111-1-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-111-111-111-1-1-111-1-1-11111-1-111-1-11-1111-1-111-1-111-1-1-1-111
χ141111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-111-1-1-111-111-1-1-11111-1-1-1-111-111-1-1111111-1-1-1-111-1-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-111-111-1-1-1-1-11-1111-1-1-11-11-1-111-1-11111-1-111-11111-1-1-1-1-1-11111-1-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-11111111-11-11-1-111-11-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1-111
χ17222222-1222-122-122-122-1-12-1-1-12-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-100222200002200-1-12-12-100220000-1-1-1-1-1-1-1-102000-1-10000-1-1000000
χ18222222-1222-122-122-122-1-12-1-1-12-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-10022-2-20000-2-200-1-1-21-2100220000-1-1-1-111110-200011000011000000
χ19222222-1222-122-122-122-1-12-1-1-12-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-2220000-2-200112-12-100-2-200001111-1-1-1-10-200011000011000000
χ20222222-1222-122-122-122-1-12-1-1-12-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-2-2-20000220011-21-2100-2-200001111111102000-1-10000-1-1000000
χ21222222-1-2-22-122-122-122-1-12-1-1-12-12-1-1-2-2-2-211-1-1-1-1-2-211111111002-22-200002200-112-1-21002-20000-1-111-1-1110-2000110000-1-1000000
χ22222222-1-2-22-122-122-122-1-12-1-1-12-12-1-1-2-2-2-211-1-1-1-1-2-211111111002-2-220000-2-200-11-212-1002-20000-1-11111-1-102000-1-1000011000000
χ23222222-1-2-22-122-122-122-1-12-1-1-12-12-1-1-2-2-2-211-1-1-1-1-2-21111111100-222-20000-2-2001-12-1-2100-22000011-1-1-1-11102000-1-1000011000000
χ24222222-1-2-22-122-122-122-1-12-1-1-12-12-1-1-2-2-2-211-1-1-1-1-2-21111111100-22-22000022001-1-212-100-22000011-1-111-1-10-2000110000-1-1000000
χ2522222-1222-122-122-122-12-1-12-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1220022002200-1-100-12-122200-1-1-1-10000-1-1-1-1200-1-10000-1-100000000
χ2622222-1222-122-122-122-12-1-12-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-12200-2-200-2-200-1-1001-21-22200-1-1-1-100001111-2001100001100000000
χ2722222-1222-122-122-122-12-1-12-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2002200-2-2001100-12-12-2-20011110000-1-1-1-1-2001100001100000000
χ2822222-1222-122-122-122-12-1-12-1-1-12-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-200220011001-21-2-2-200111100001111200-1-10000-1-100000000
χ2922222-12-2-2-122-122-122-12-1-12-1-1-12-12-1-2-211-2-2-1-1-1-111-2-21111112-2002-2002200-1100-121-22-200-1-1110000-1-111-200110000-1-100000000
χ3022222-12-2-2-122-122-122-12-1-12-1-1-12-12-1-2-211-2-2-1-1-1-111-2-21111112-200-2200-2-200-11001-2-122-200-1-111000011-1-1200-1-100001100000000
χ3122222-12-2-2-122-122-122-12-1-12-1-1-12-12-1-2-211-2-2-1-1-1-111-2-2111111-22002-200-2-2001-100-121-2-220011-1-10000-1-111200-1-100001100000000
χ3222222-12-2-2-122-122-122-12-1-12-1-1-12-12-1-2-211-2-2-1-1-1-111-2-2111111-2200-220022001-1001-2-12-220011-1-1000011-1-1-200110000-1-100000000
χ332222-1222222-122-122-1-1-12-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-122220022000022220000-1-1-1-1-1-1-1-1-1-1-1-100000020000-1-10000-1-10000
χ342222-1222222-122-122-1-1-12-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-2-200-2-2000022-2-20000-1-111-1-1-1-11111000000-20000110000110000
χ352222-1222222-122-122-1-1-12-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-22200-2-20000-2-222000011-1-11111-1-1-1-1000000-20000110000110000
χ362222-1222222-122-122-1-1-12-1-122-1-1-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-200220000-2-2-2-2000011111111111100000020000-1-10000-1-10000
χ372222-122-2-222-122-122-1-1-12-1-122-1-1-1-1211-2-2-2-2-1-1-1-11111-2-211112-22-2002200002-22-20000-11-11-1-111-1-111000000-20000110000-1-10000
χ382222-122-2-222-122-122-1-1-12-1-122-1-1-1-1211-2-2-2-2-1-1-1-11111-2-211112-2-2200-2-200002-2-220000-111-1-1-11111-1-100000020000-1-10000110000
χ392222-122-2-222-122-122-1-1-12-1-122-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-222-200-2-20000-222-200001-1-1111-1-1-1-11100000020000-1-10000110000
χ402222-122-2-222-122-122-1-1-12-1-122-1-1-1-1211-2-2-2-2-1-1-1-11111-2-21111-22-2200220000-22-2200001-11-111-1-111-1-1000000-20000110000-1-10000
χ4122-2-222200-2-2-222-2-2-22222-2-22-2-2-222-200000022-2-200000000000000002-22i−2i2i−2i0000000000000000000000000000000002i−2i2i−2i2-20000
χ4222-2-222200-2-2-222-2-2-22222-2-22-2-2-222-200000022-2-200000000000000002-2−2i2i−2i2i000000000000000000000000000000000−2i2i−2i2i2-20000
χ4322-2-222200-2-2-222-2-2-22222-2-22-2-2-222-200000022-2-20000000000000000-222i−2i−2i2i0000000000000000000000000000000002i−2i−2i2i-220000
χ4422-2-222200-2-2-222-2-2-22222-2-22-2-2-222-200000022-2-20000000000000000-22−2i2i2i−2i000000000000000000000000000000000−2i2i2i−2i-220000
χ452-22-22222-2-2-22-2-2-222-2222-2-2-2-222-2-222-22-22-22-2-222-22-22-222-2-20000000000000000000000000000000000000000000000000002i−2i2i−2i
χ462-22-22222-2-2-22-2-2-222-2222-2-2-2-222-2-222-22-22-22-2-222-22-22-222-2-2000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ472-22-2222-22-2-22-2-2-222-2222-2-2-2-222-2-22-22-22-222-2-22-22-22-22-2-2220000000000000000000000000000000000000000000000000002i−2i−2i2i
χ482-22-2222-22-2-22-2-2-222-2222-2-2-2-222-2-22-22-22-222-2-22-22-22-22-2-222000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ4944444-2-244-2-24-2-24-2-24-2-21-2-211-2-2-2-2144-2-2-2-21111-2-2-2-21111110000440000000000-2-2-2-200000000000011110000000000000000000
χ5044444-2-244-2-24-2-24-2-24-2-21-2-211-2-2-2-2144-2-2-2-21111-2-2-2-21111110000-4-400000000002222000000000000-1-1-1-10000000000000000000
χ5144444-2-2-4-4-2-24-2-24-2-24-2-21-2-211-2-2-2-21-4-4222211112222-1-1-1-1-1-100004-40000000000-2-22200000000000011-1-10000000000000000000
χ5244444-2-2-4-4-2-24-2-24-2-24-2-21-2-211-2-2-2-21-4-4222211112222-1-1-1-1-1-10000-44000000000022-2-2000000000000-1-1110000000000000000000
χ534444-24-2444-2-24-2-24-2-2-21-2-21-2-2-21-21-2-2-244-2-21111-2-211-2-2111100440000000000-2-2000000-2-20000111100000000000000000000000
χ544444-24-2444-2-24-2-24-2-2-21-2-21-2-2-21-21-2-2-244-2-21111-2-211-2-2111100-4-4000000000022000000220000-1-1-1-100000000000000000000000
χ554444-24-2-4-44-2-24-2-24-2-2-21-2-21-2-2-21-21-222-4-422111122-1-122-1-1-1-1004-40000000000-22000000-22000011-1-100000000000000000000000
χ564444-24-2-4-44-2-24-2-24-2-2-21-2-21-2-2-21-21-222-4-422111122-1-122-1-1-1-100-4400000000002-20000002-20000-1-11100000000000000000000000
χ574444-2-2444-24-2-24-2-24-21-2-21-2-2-21-21-2-2-2-2-2-244111111-2-2-2-21111440000000000-2-2000000-2-2001111000000000000000000000000000
χ584444-2-2444-24-2-24-2-24-21-2-21-2-2-21-21-2-2-2-2-2-244111111-2-2-2-21111-4-40000000000220000002200-1-1-1-1000000000000000000000000000
χ594444-2-24-4-4-24-2-24-2-24-21-2-21-2-2-21-21-2-22222-4-41111-1-12222-1-1-1-14-40000000000-22000000-220011-1-1000000000000000000000000000
χ604444-2-24-4-4-24-2-24-2-24-21-2-21-2-2-21-21-2-22222-4-41111-1-12222-1-1-1-1-4400000000002-20000002-200-1-111000000000000000000000000000
χ6144-4-444-200-42-44-2-4-4244-2-2-42-22-424-22000000-2-222000000000000000000004i−4i00000000000000000000000000000000000−2i2i000000
χ6244-4-444-200-42-44-2-4-4244-2-2-42-22-424-22000000-2-22200000000000000000000−4i4i000000000000000000000000000000000002i−2i000000
χ6344-4-44-24002-4-4-24-42-44-24-22-4-222-4-242000000-2-2220000000000000000004i−4i00000000000000000000000000000000000−2i2i00000000
χ6444-4-44-24002-4-4-24-42-44-24-22-4-222-4-242000000-2-222000000000000000000−4i4i000000000000000000000000000000000002i−2i00000000
χ6544-4-4-24400-4-42442-4-4-2-2-24224-422-2-2-4000000-2-22200000000000000004-400000000000000000000000000000000000000000-220000
χ6644-4-4-24400-4-42442-4-4-2-2-24224-422-2-2-4000000-2-2220000000000000000-44000000000000000000000000000000000000000002-20000
χ674-44-444-24-4-424-42-44-2-44-2-2-42224-2-42-24-44-4-22-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000000000
χ684-44-444-2-44-424-42-44-2-44-2-2-42224-2-42-2-44-442-2-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000000000
χ694-44-44-244-42-442-4-4-24-4-24-22-422-242-4-24-4-224-4-222-2-224-4-22-2-2220000000000000000000000000000000000000000000000000000000
χ704-44-44-24-442-442-4-4-24-4-24-22-422-242-4-2-442-2-44-222-22-2-442-222-2-20000000000000000000000000000000000000000000000000000000
χ714-44-44-2-24-422422-4-2-2-4-2-2122-1-1-2-22214-4-22-221-1-11-22-221-111-1-1000000000000000000000000000000003-33-30000000000000000000
χ724-44-44-2-24-422422-4-2-2-4-2-2122-1-1-2-22214-4-22-221-1-11-22-221-111-1-100000000000000000000000000000000-33-330000000000000000000
χ734-44-44-2-2-4422422-4-2-2-4-2-2122-1-1-2-2221-442-22-21-1-112-22-2-11-1-111000000000000000000000000000000003-3-330000000000000000000
χ744-44-44-2-2-4422422-4-2-2-4-2-2122-1-1-2-2221-442-22-21-1-112-22-2-11-1-11100000000000000000000000000000000-333-30000000000000000000
χ754-44-4-2444-4-4-4-2-4-42442-2-2422-4-4-2-2224-224-44-4-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000000000
χ764-44-4-244-44-4-4-2-4-42442-2-2422-4-4-2-22242-2-44-44-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000000000000
χ774-44-4-24-24-4-42-2-4224-22-21-22-122-212-1-2-224-4-221-1-11-221-1-2211-1-100000000000000000000000000003i−3i3i−3i00000000000000000000000
χ784-44-4-24-24-4-42-2-4224-22-21-22-122-212-1-2-224-4-221-1-11-221-1-2211-1-10000000000000000000000000000−3i3i−3i3i00000000000000000000000
χ794-44-4-24-2-44-42-2-4224-22-21-22-122-212-1-22-2-442-21-1-112-2-112-2-1-11100000000000000000000000000003i−3i−3i3i00000000000000000000000
χ804-44-4-24-2-44-42-2-4224-22-21-22-122-212-1-22-2-442-21-1-112-2-112-2-1-1110000000000000000000000000000−3i3i3i−3i00000000000000000000000
χ814-44-4-2-244-42-4-22-42-2421-2-2-12221-2-12-2-22-224-41-1-111-1-22-2211-1-10000000000000000000000003i−3i3i−3i000000000000000000000000000
χ824-44-4-2-244-42-4-22-42-2421-2-2-12221-2-12-2-22-224-41-1-111-1-22-2211-1-1000000000000000000000000−3i3i−3i3i000000000000000000000000000
χ834-44-4-2-24-442-4-22-42-2421-2-2-12221-2-12-22-22-2-441-1-11-112-22-2-1-1110000000000000000000000003i−3i−3i3i000000000000000000000000000
χ844-44-4-2-24-442-4-22-42-2421-2-2-12221-2-12-22-22-2-441-1-11-112-22-2-1-111000000000000000000000000−3i3i3i−3i000000000000000000000000000
χ854-4-444440044-4-4-44-4-4-444444-44-4-4-4-4-40000004-44-400000000000000000000000000000000000000000000000000000000000000000
χ864-4-4444-2004-2-4-424-42-44-2-24-22-2-42-422000000-22-22000000000000000000000000000000000000000000000000000−2i32i3000000000000
χ874-4-4444-2004-2-4-424-42-44-2-24-22-2-42-422000000-22-220000000000000000000000000000000000000000000000000002i3−2i3000000000000
χ884-4-444-2400-24-42-442-4-4-24-2-242-22-42-42000000-22-220000000000000000000000000000000000000000000000000−2i32i300000000000000
χ894-4-444-2400-24-42-442-4-4-24-2-242-22-42-42000000-22-2200000000000000000000000000000000000000000000000002i3−2i300000000000000
χ904-4-44-24400442-4-4-2-4-42-2-24-2-2-442222-4000000-22-2200000000000000000000000000000000000000000000000000000−2i32i30000000000
χ914-4-44-24400442-4-4-2-4-42-2-24-2-2-442222-4000000-22-22000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ928888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9488-8-88-4-40044-8-4-4-8448-4-42442-244-4-4-200000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-48-400-8448-44-84-4-42-44-2-444-2-42400000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-48004-84-4844-8-42-4-4-24-44-242-4400000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-400444-4-4444-4222-2-22-2-2-222-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-400444-4-4444-4222-2-22-2-2-222-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-48-844-4444-4-44222-2-2-2-222-2-22-44-44-44-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4-8844-4444-4-44222-2-2-2-222-2-224-44-44-4-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000000
χ1018-8-888-4-400-4-4-844844-8-4-42-4-4-224444-20000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-4008-44-84-4-844-42-4-424-44-24-240000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-4800-4844-8-44-842-4-42-44-4-24-2440000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-400-4-4444-444422222-22-2-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-400-4-4444-444422222-22-2-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).