Finite Group Databasebeta

← Group #13156305

Character table — Group #13156305

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222222444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636363636363636363636363636108108
order12223334466666666633366666666612121212121236661212121212121212121222444466666666121212121212121212121212121212124888812121212242424242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111111-1-11-11111111111-1-111-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ511111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1
χ711111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-111
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002200000000000000000000000000-2000022-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200-2-20000000000000000000000000020000-2-2220000000000
χ11222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-122000222-1-1-1-1-1-100-1-100220000-1-1-1-10002200000000-1-1-1-100
χ12222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-122000-222-1-1-1-1-1-1001100-2-200001111000-2-200000000111100
χ13222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-20002-2-211111100-1-100220000-1-1-1-1000-2-200000000111100
χ14222222-1222-122-12-1222-1-12-1-1-12-1-12-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2000-2-2-2111111001100-2-2000011110002200000000-1-1-1-100
χ1522222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-1220020-1-122-1-1-1-1-1-1002200-1-1-1-10000022000000-1-1-1-1000000
χ1622222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-12200-20-1-122-1-1-1-11100-2-200111100000-2-20000001111000000
χ1722222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2-2002011-2-21111-1-1002200-1-1-1-100000-2-20000001111000000
χ1822222-1222-122-12-1222-12-1-12-1-1-12-1-1222-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2011-2-211111100-2-20011110000022000000-1-1-1-1000000
χ192222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1002222000000002222-1-1-1-1-1-1-1-1-1-1-1-120000-1-1-1-10000000000
χ202222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-10022-2-200000000-2-2-2-211111111111120000-1-1-1-10000000000
χ212222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-100-2-22-20000000022-2-2-1-111-1-1-1-11111-2000011110000000000
χ222222-1222222-12222-1-1-1-12-1-122-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2200000000-2-22211-1-11111-1-1-1-1-2000011110000000000
χ232222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-21111002200000000000000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3-20000-1-1110000000000
χ242222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-21111002200000000000000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3-20000-1-1110000000000
χ252222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-2111100-2-200000000000000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i32000011-1-10000000000
χ262222-122-2-222-12222-1-1-1-12-1-122-1-12-1-111-2-2-2-2-1-1-1-11111-2-2111100-2-200000000000000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i32000011-1-10000000000
χ2722-2-22222-2-2-2222-2-2-2-2222-2-2-2-2222-2-22-222-2-22-2-222-22-22-222-2-22-200002-22-222-2-200000000000000000000000000000000000
χ2822-2-22222-2-2-2222-2-2-2-2222-2-2-2-2222-2-22-222-2-22-2-222-22-22-222-2-2-220000-22-22-2-22200000000000000000000000000000000000
χ2922-2-2222-22-2-2222-2-2-2-2222-2-2-2-2222-2-2-22-2-2222-2-22-22-22-22-2-222000000000000000000000000000000000000000000000002i−2i
χ3022-2-2222-22-2-2222-2-2-2-2222-2-2-2-2222-2-2-22-2-2222-2-22-22-22-22-2-22200000000000000000000000000000000000000000000000−2i2i
χ3122-2-222-12-2-2122-1-21-2-22-1-1-21112-1-1-212-22-1-21-111-12-2-11-11-1-1112-200002-2-11-1-111003−3000000003−33−3000000000000033−3−300
χ3222-2-222-12-2-2122-1-21-2-22-1-1-21112-1-1-212-22-1-21-111-12-2-11-11-1-1112-200002-2-11-1-11100−3300000000−33−330000000000000−3−33300
χ3322-2-222-12-2-2122-1-21-2-22-1-1-21112-1-1-212-22-1-21-111-12-2-11-11-1-111-220000-221-111-1-1003−3000000003−33−30000000000000−3−33300
χ3422-2-222-12-2-2122-1-21-2-22-1-1-21112-1-1-212-22-1-21-111-12-2-11-11-1-111-220000-221-111-1-100−3300000000−33−33000000000000033−3−300
χ3522-2-22-122-21-22-121-2-2-2-12-11-211-12-11-22-2-121-2-111-1-112-2-11-1-1112-20000-112-2-1-1113−30000003−33−3000000000000033−3−3000000
χ3622-2-22-122-21-22-121-2-2-2-12-11-211-12-11-22-2-121-2-111-1-112-2-11-1-1112-20000-112-2-1-111−33000000−33−330000000000000−3−333000000
χ3722-2-22-122-21-22-121-2-2-2-12-11-211-12-11-22-2-121-2-111-1-112-2-11-1-111-2200001-1-2211-1-13−30000003−33−30000000000000−3−333000000
χ3822-2-22-122-21-22-121-2-2-2-12-11-211-12-11-22-2-121-2-111-1-112-2-11-1-111-2200001-1-2211-1-1−33000000−33−33000000000000033−3−3000000
χ392-2-222220022-2-2-2-2-22-2222222-2-2-2-2-2-200000022-2-20000000000002-2000000000000000000000000000−i2i2−i2i22-200−i2i2−i2i2−i2i2−i2i200
χ402-2-222220022-2-2-2-2-22-2222222-2-2-2-2-2-200000022-2-20000000000002-2000000000000000000000000000i2−i2i2−i22-200i2−i2i2−i2i2−i2i2−i200
χ412-2-222220022-2-2-2-2-22-2222222-2-2-2-2-2-200000022-2-2000000000000-22000000000000000000000000000−i2i2i2−i2-2200−i2i2−i2i2i2−i2i2−i200
χ422-2-222220022-2-2-2-2-22-2222222-2-2-2-2-2-200000022-2-2000000000000-22000000000000000000000000000i2−i2−i2i2-2200i2−i2i2−i2−i2i2−i2i200
χ43444444-2-4-44-244-24-2444-2-24-2-2-24-2-24-2-4-4-42-42-2-2-2-2-4-4222222220000000000000000000000000000000000000000000000000
χ4444444-24-4-4-244-24-2444-24-2-24-2-2-24-2-24-4-42-42-4-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000
χ4544444-2-244-2-24-2-2-2-244-2-21-2-211-2-21-2-244-2-2-2-21111-2-2-2-2111111440000-2-2-2-2111100000000000000000000000000000000000
χ4644444-2-244-2-24-2-2-2-244-2-21-2-211-2-21-2-244-2-2-2-21111-2-2-2-2111111-4-400002222-1-1-1-100000000000000000000000000000000000
χ4744444-2-2-4-4-2-24-2-2-2-244-2-21-2-211-2-21-2-2-4-4222211112222-1-1-1-1-1-100000000003-33-300000000000000000000000000000000000
χ4844444-2-2-4-4-2-24-2-2-2-244-2-21-2-211-2-21-2-2-4-4222211112222-1-1-1-1-1-10000000000-33-3300000000000000000000000000000000000
χ494444-24-2444-2-24-24-2-2-2-21-2-21-2-2-21-2-21-2-24-24-21111-2-211-2-211110000040000000000-2-200-2-2000011110000000000000000000
χ504444-24-2444-2-24-24-2-2-2-21-2-21-2-2-21-2-21-2-24-24-21111-2-211-2-2111100000-400000000002200220000-1-1-1-10000000000000000000
χ514444-24-2-4-44-2-24-24-2-2-2-21-2-21-2-2-21-2-2122-42-42111122-1-122-1-1-1-100000000000000000000−2i32i30000i3i3−i3−i30000000000000000000
χ524444-24-2-4-44-2-24-24-2-2-2-21-2-21-2-2-21-2-2122-42-42111122-1-122-1-1-1-1000000000000000000002i3−2i30000−i3−i3i3i30000000000000000000
χ534444-2-2444-24-2-24-24-2-21-2-21-2-2-21-2-21-2-2-2-24-24111111-2-2-2-2111100004000000000-2-200-2-200111100000000000000000000000
χ544444-2-2444-24-2-24-24-2-21-2-21-2-2-21-2-21-2-2-2-24-24111111-2-2-2-211110000-400000000022002200-1-1-1-100000000000000000000000
χ554444-2-24-4-4-24-2-24-24-2-21-2-21-2-2-21-2-21-2222-42-41111-1-12222-1-1-1-1000000000000000000−2i32i300i3i3−i3−i300000000000000000000000
χ564444-2-24-4-4-24-2-24-24-2-21-2-21-2-2-21-2-21-2222-42-41111-1-12222-1-1-1-10000000000000000002i3−2i300−i3−i3i3i300000000000000000000000
χ5744-4-444-2-44-4244-2-42-4-44-2-2-42224-2-2-42-44-424-2-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000
χ5844-4-44-24-442-44-242-4-4-4-24-22-422-24-22-4-442-4-24-222-22-2-442-222-2-20000000000000000000000000000000000000000000000000
χ5944-4-44-2-24-4224-2-222-4-4-2-2122-1-1-2-21224-4-2-2221-1-11-22-221-111-1-14-40000-22-2211-1-100000000000000000000000000000000000
χ6044-4-44-2-24-4224-2-222-4-4-2-2122-1-1-2-21224-4-2-2221-1-11-22-221-111-1-1-4400002-22-2-1-11100000000000000000000000000000000000
χ6144-4-44-2-2-44224-2-222-4-4-2-2122-1-1-2-2122-4422-2-21-1-112-22-2-11-1-11100000000003-3-3300000000000000000000000000000000000
χ6244-4-44-2-2-44224-2-222-4-4-2-2122-1-1-2-2122-4422-2-21-1-112-22-2-11-1-1110000000000-333-300000000000000000000000000000000000
χ6344-4-4-2444-4-4-4-244-4-422-2-2422-4-4-2-2422-2244-4-4-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000
χ6444-4-4-244-44-4-4-244-4-422-2-2422-4-4-2-24222-2-4-444-222-22-22-2-4422-2-20000000000000000000000000000000000000000000000000
χ6544-4-4-24-24-4-42-24-2-4222-21-22-122-21-22-1-224-2-421-1-11-221-1-2211-1-1000000000000000023−2300000000−33−330000000000000000000
χ6644-4-4-24-24-4-42-24-2-4222-21-22-122-21-22-1-224-2-421-1-11-221-1-2211-1-10000000000000000−2323000000003−33−30000000000000000000
χ6744-4-4-24-2-44-42-24-2-4222-21-22-122-21-22-12-2-424-21-1-112-2-112-2-1-111000000000000000000000000003i−3i−3i3i0000000000000000000
χ6844-4-4-24-2-44-42-24-2-4222-21-22-122-21-22-12-2-424-21-1-112-2-112-2-1-11100000000000000000000000000−3i3i3i−3i0000000000000000000
χ6944-4-4-2-244-42-4-2-242-4221-2-2-12221-2-2-12-22-242-41-1-111-1-22-2211-1-10000000000000023−23000000−33−3300000000000000000000000
χ7044-4-4-2-244-42-4-2-242-4221-2-2-12221-2-2-12-22-242-41-1-111-1-22-2211-1-100000000000000−23230000003−33−300000000000000000000000
χ7144-4-4-2-24-442-4-2-242-4221-2-2-12221-2-2-122-22-4-241-1-11-112-22-2-1-11100000000000000000000003i−3i−3i3i00000000000000000000000
χ7244-4-4-2-24-442-4-2-242-4221-2-2-12221-2-2-122-22-4-241-1-11-112-22-2-1-1110000000000000000000000−3i3i3i−3i00000000000000000000000
χ734-44-444400-4-4-4-4-444-44444-4-4-44-4-4-4440000004-44-400000000000000000000000000000000000000000000000000000000000
χ744-44-444-200-42-4-424-2-444-2-2-422-2-4224-2000000-22-2200000000000000000000000000000000000000000000000000000i6−i6−i6i600
χ754-44-444-200-42-4-424-2-444-2-2-422-2-4224-2000000-22-2200000000000000000000000000000000000000000000000000000−i6i6i6−i600
χ764-44-44-24002-4-42-4-24-44-24-22-42-22-42-24000000-22-220000000000000000000000000000000000000000000000000i6−i6−i6i6000000
χ774-44-44-24002-4-42-4-24-44-24-22-42-22-42-24000000-22-220000000000000000000000000000000000000000000000000−i6i6i6−i6000000
χ784-44-4-24400-4-42-4-4442-2-2-2422-4422-4-2-2000000-22-2200000000000000000000000000000000000000000000000−2i32i30000000000
χ794-44-4-24400-4-42-4-4442-2-2-2422-4422-4-2-2000000-22-22000000000000000000000000000000000000000000000002i3−2i30000000000
χ804-4-4444-2004-2-4-42-424-44-2-24-2-22-422-42000000-2-2220000000000000000000000000000000000000000000−2i22i200000000i2−i2i2−i200
χ814-4-4444-2004-2-4-42-424-44-2-24-2-22-422-42000000-2-22200000000000000000000000000000000000000000002i2−2i200000000−i2i2−i2i200
χ824-4-444-2400-24-42-42-44-4-24-2-24-222-422-4000000-2-22200000000000000000000000000000000000000000−2i22i2000000i2−i2i2−i2000000
χ834-4-444-2400-24-42-42-44-4-24-2-24-222-422-4000000-2-222000000000000000000000000000000000000000002i2−2i2000000−i2i2−i2i2000000
χ844-4-44-24400442-4-4-4-4-22-2-24-2-24-422-422000000-2-2220000000000004-40000000000000000000000000000000-22000000000000
χ854-4-44-24400442-4-4-4-4-22-2-24-2-24-422-422000000-2-222000000000000-4400000000000000000000000000000002-2000000000000
χ868888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000
χ878888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000
χ8888-8-8-4-4-48-844-4-4-44444222-2-2-2-2222-2-2-44-4-444-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000
χ8988-8-8-4-4-4-8844-4-4-44444222-2-2-2-2222-2-24-444-4-4-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000
χ908-88-88-4-40044-844-4-4-88-4-4244-2244-2-4-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ918-88-8-48-400-844-848-44-4-42-44-24-44-24-420000002-22-200000000000000000000000000000000000000000000000000000000000
χ928-88-8-4-48004-844-8-484-42-4-4-244-4-2442-40000002-22-200000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-1100000033−3333−330000000000000000000000000000000000000000000000000
χ948-88-8-4-4-40044444-4-44-4222-2-2-22-2-2-222000000-11-11000000−3333−33330000000000000000000000000000000000000000000000000
χ958-8-888-4-400-4-4-844448-8-4-42-4-42-244-24400000022-2-200000000000000000000000000000000000000000000000000000000000
χ968-8-88-48-4008-44-84-84-44-42-4-42-444-244-200000022-2-200000000000000000000000000000000000000000000000000000000000
χ978-8-88-4-4800-4844-84-8-442-4-42-4-44-244-2400000022-2-200000000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-400-4-444444-44222222-2-2-2-2-2-2000000-1-11100000033−33−33330000000000000000000000000000000000000000000000000
χ998-8-88-4-4-400-4-444444-44222222-2-2-2-2-2-2000000-1-111000000−333333−330000000000000000000000000000000000000000000000000

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