Finite Group Databasebeta

← Group #13168546

Character table — Group #13168546

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121244444121212121212121244121212121212121212121212121212121212121224444661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111-1-1-111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-111111-1-11111-1-111-1-1-11111111-1-1-1-111111-1-11-111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-111-1-111-1-11111-1-1111111-1-1-1-111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1-1-11-1-11-111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111111111-1-11-1-11-1-111-1-111-1-111-1-11-11-1-1111111-1-111-1-1-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-111-1-1111-1-111-1-111-1-1-111
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1-1-1-1111-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-11-11
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-111-11111-1-1-1-111-1-111-11-11-1-1-1-1-111-1-11111-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-11111111-1-11-1-1-1-11111-1-111-1-1-11-11-1-1-1-1-111-1-1-1-1111
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111-1-1-1-1-1-1111-1-1-111-1-11111-1-1-1-11111-1-1111-1-1-1-111111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-111-1111-1-1-1-111-1-11111-1-1-1-1111-1-111-1-11111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111-111-111-1-111-1-111-1-1111-11-1-1111111-1-1-1-1-1-11
χ17222222-1-122-12222-12-1-122-1-12-1-1-12-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1002222200-1-1-1-100-1200022-1-1-1-1-10000-1-1-1-120020-1-1000000000-10
χ18222222-1-122-12222-12-1-122-1-12-1-1-12-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1002-2-22200-1-11100-12000-2-21-1-1-1-100001111-200-201100000000010
χ19222222-1-122-12222-12-1-122-1-12-1-1-12-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-100-222-2-20011-1-1001-200022-111110000-1-1-1-1-200-201100000000010
χ20222222-1-122-12222-12-1-122-1-12-1-1-12-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-100-2-2-2-2-2001111001-2000-2-2111110000111120020-1-1000000000-10
χ21222222-1-122-12222-12-1-1-22-1-12-1-1-12-1-2-222-1-1-1-11-2-2-21111111100-22-22200-1-1-1-1001-20002-21-1-1110000-1-111200-20-1-100000000010
χ22222222-1-122-12222-12-1-1-22-1-12-1-1-12-1-2-222-1-1-1-11-2-2-21111111100-2-222200-1-111001-2000-22-1-1-111000011-1-1-2002011000000000-10
χ23222222-1-122-12222-12-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-11-2-2-2111111110022-2-2-20011-1-100-120002-2111-1-10000-1-111-2002011000000000-10
χ24222222-1-122-12222-12-1-1-22-1-12-1-1-12-1-2-2-2-2-1-1-1-11-2-2-211111111002-22-2-200111100-12000-22-111-1-1000011-1-1200-20-1-100000000010
χ2522222-1222-12-122-12-12-12-12-1-12-1-1-122222-1-1-1-12-1-1-122-1-1-1-1-1-122200-1-1-1-12200002-122-1000-1-1-1-1-1-1-1-100000220000-1-1000000-100
χ2622222-1222-12-122-12-12-12-12-1-12-1-1-122222-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2200-1-1112200002-1-2-21000-1-1-1-1111100000-2-2000011000000100
χ2722222-1222-12-122-12-12-12-12-1-12-1-1-1222-2-2-1-1-1-12-1-1-122-1-1-1-1-1-122-20011-1-1-2-20000-2122-10001111-1-1-1-100000-2-2000011000000100
χ2822222-1222-12-122-12-12-12-12-1-12-1-1-1222-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2001111-2-20000-21-2-210001111111100000220000-1-1000000-100
χ2922222-1222-12-122-12-12-1-2-12-1-12-1-1-12-2-222-1-1-1-1-2111-2-21111112-2-200-1-1-1-1220000-212-21000-1-111-1-11100000-220000-1-1000000100
χ3022222-1222-12-122-12-12-1-2-12-1-12-1-1-12-2-222-1-1-1-1-2111-2-2111111-22-200-1-111220000-21-22-1000-1-11111-1-1000002-2000011000000-100
χ3122222-1222-12-122-12-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-1-2111-2-21111112-220011-1-1-2-200002-12-2100011-1-1-1-111000002-2000011000000-100
χ3222222-1222-12-122-12-12-1-2-12-1-12-1-1-12-2-2-2-2-1-1-1-1-2111-2-2111111-222001111-2-200002-1-22-100011-1-111-1-100000-220000-1-1000000100
χ332222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-122022002200222200-1-12-1-120000-1-1-1-1-1-1-1-1000020000-1-1-1-100000
χ342222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1220-2-2002200-2-2-2-200-1-1211-20000-1-1-1-111110000-20000111100000
χ352222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1-2-202200-2-20022-2-20011-2-1-1200001111-1-1-1-10000-20000111100000
χ362222-1222-1222-1-122-1-122-1-12-1-122-1-1-1-100-1-1-1-122-1-1-1-122-1-1-1-1-2-20-2-200-2-200-2-2220011-211-2000011111111000020000-1-1-1-100000
χ372222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211112-202-2002200222200-11-2-11-20000-1-111-1-1110000-20000-1-11100000
χ382222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-211112-20-22002200-2-2-2-200-11-21-120000-1-11111-1-100002000011-1-100000
χ392222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-21111-2202-200-2-20022-2-2001-12-11-2000011-1-1-1-11100002000011-1-100000
χ402222-1222-1222-1-122-1-12-2-1-12-1-122-1-11100-1-1-1-1-2-21111-2-21111-220-2200-2-200-2-222001-121-12000011-1-111-1-10000-20000-1-11100000
χ412-2-22222-2-22-2-22-2-2222202-2-2-2-22-2-22002-222-2-2000000000000000002-2002-2002i−2i000000002-200000000000000000002i−2i002i−2i000
χ422-2-22222-2-22-2-22-2-2222202-2-2-2-22-2-22002-222-2-2000000000000000002-2002-200−2i2i000000002-20000000000000000000−2i2i00−2i2i000
χ432-2-22222-2-22-2-22-2-2222202-2-2-2-22-2-2200-2222-2-200000000000000000-2200-22002i−2i00000000-2200000000000000000002i−2i00−2i2i000
χ442-2-22222-2-22-2-22-2-2222202-2-2-2-22-2-2200-2222-2-200000000000000000-2200-2200−2i2i00000000-220000000000000000000−2i2i002i−2i000
χ4544444-2-2-24-2-2-244-2-2-2-214-2-21-2-211-2-244441111-2-2-2-2-2-211111100400-2-200-2-20000-2-2000000111100000000000000000000000000
χ4644444-2-2-24-2-2-244-2-2-2-214-2-21-2-211-2-244-4-41111-2-2-2-2-2-211111100-400220022000022000000-1-1-1-100000000000000000000000000
χ4744444-2-2-24-2-2-244-2-2-2-21-4-2-21-2-211-2-2-4-4441111222222-1-1-1-1-1-100-400-2-200-2-200002200000011-1-100000000000000000000000000
χ4844444-2-2-24-2-2-244-2-2-2-21-4-2-21-2-211-2-2-4-4-4-41111222222-1-1-1-1-1-1004002200220000-2-2000000-1-11100000000000000000000000000
χ494444-24-2-2-24-24-2-24-2-21-24-21-2-21-2-2-21-2-2001111-24-2-211-2-2111100044000000-2-20000000-2-2-2000000001111000000000000000000
χ504444-24-2-2-24-24-2-24-2-21-24-21-2-21-2-2-21-2-2001111-24-2-211-2-21111000-4-400000022000000022200000000-1-1-1-1000000000000000000
χ514444-24-2-2-24-24-2-24-2-21-2-4-21-2-21-2-2-21220011112-422-1-122-1-1-1-10004-4000000-2-20000000-2220000000011-1-1000000000000000000
χ524444-24-2-2-24-24-2-24-2-21-2-4-21-2-21-2-2-21220011112-422-1-122-1-1-1-1000-440000002200000002-2-200000000-1-111000000000000000000
χ534444-2-244-2-24-2-2-2-241-2-241-2-21-2-2-21-2-2-20011114-211-2-2-2-211114400000-2-200000000-2-2-2000000011110000000000000000000000
χ544444-2-244-2-24-2-2-2-241-2-241-2-21-2-2-21-2-2-20011114-211-2-2-2-21111-4-40000022000000002220000000-1-1-1-10000000000000000000000
χ554444-2-244-2-24-2-2-2-241-2-2-41-2-21-2-2-21-222001111-42-1-12222-1-1-1-14-400000-2-200000000-222000000011-1-10000000000000000000000
χ564444-2-244-2-24-2-2-2-241-2-2-41-2-21-2-2-21-222001111-42-1-12222-1-1-1-1-440000022000000002-2-20000000-1-1110000000000000000000000
χ5744-4-44444-4-4-4-4-444-44440-444-4-4-4-44-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-2-4-42-4-44424-2-20-4-2-2-4222420000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ5944-4-444-2-2-4-42-4-44424-2-20-4-2-2-4222420000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ6044-4-44-244-42-42-44-2-4-24-2024-22-422-2-40000-22-2200000000000000000000000000000000000000000000000000000023−23000000000
χ6144-4-44-244-42-42-44-2-4-24-2024-22-422-2-40000-22-22000000000000000000000000000000000000000000000000000000−2323000000000
χ6244-4-4-24442-4-4-42-24-4-2-2402-2422-4-4-220000-22-22000000000000000000000000000000000000000000000000000000000023−2300000
χ6344-4-4-24442-4-4-42-24-4-2-2402-2422-4-4-220000-22-220000000000000000000000000000000000000000000000000000000000−232300000
χ644-44-4444-44-444-4-4-4-44440-4-4-444-44-4-400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ654-44-444-224-4-24-4-4-424-2-20-4224-22-2-420000-222-20000000000000000000000023−2300000000000000000023−2300000000000000000000
χ664-44-444-224-4-24-4-4-424-2-20-4224-22-2-420000-222-200000000000000000000000−2323000000000000000000−232300000000000000000000
χ674-44-44-24-4424-2-4-42-4-24-202-42-242-22-40000-222-2000000000000000000023−2300000000000000000023−23000000000000000000000000
χ684-44-44-24-4424-2-4-42-4-24-202-42-242-22-40000-222-20000000000000000000−2323000000000000000000−2323000000000000000000000000
χ694-44-4-244-4-2-44422-4-4-2-24022-4-2-2-4422−2i32i300-222-200−2i32i3−2i32i300−2i3−2i32i32i300000000000000000000000000000000000000000000000000000
χ704-44-4-244-4-2-44422-4-4-2-24022-4-2-2-44222i3−2i300-222-2002i3−2i32i3−2i3002i32i3−2i3−2i300000000000000000000000000000000000000000000000000000
χ714-44-4-24-22-2-4-2422-42-21-202-12-212-22-1−2i32i3001-1-1100−2i32i3i3−i300i3i3−i3−i30000000000023−23000000000000000000−333i−3i000000000000000000
χ724-44-4-24-22-2-4-2422-42-21-202-12-212-22-1−2i32i3001-1-1100−2i32i3i3−i300i3i3−i3−i300000000000−23230000000000000000003−3−3i3i000000000000000000
χ734-44-4-24-22-2-4-2422-42-21-202-12-212-22-12i3−2i3001-1-11002i3−2i3−i3i300−i3−i3i3i30000000000023−23000000000000000000−33−3i3i000000000000000000
χ744-44-4-24-22-2-4-2422-42-21-202-12-212-22-12i3−2i3001-1-11002i3−2i3−i3i300−i3−i3i3i300000000000−23230000000000000000003−33i−3i000000000000000000
χ754-44-4-2-24-4-224-2222-41-2-20-1221-22-2-12−2i32i3001-1-1100i3−i3−2i32i300i3i3−i3−i3000000023−23000000000000000000−333i−3i0000000000000000000000
χ764-44-4-2-24-4-224-2222-41-2-20-1221-22-2-12−2i32i3001-1-1100i3−i3−2i32i300i3i3−i3−i30000000−23230000000000000000003−3−3i3i0000000000000000000000
χ774-44-4-2-24-4-224-2222-41-2-20-1221-22-2-122i3−2i3001-1-1100−i3i32i3−2i300−i3−i3i3i3000000023−23000000000000000000−33−3i3i0000000000000000000000
χ784-44-4-2-24-4-224-2222-41-2-20-1221-22-2-122i3−2i3001-1-1100−i3i32i3−2i300−i3−i3i3i30000000−23230000000000000000003−33i−3i0000000000000000000000
χ794-4-4444-22-442-44-4-4-24-2-20422-42-22-4-2004-4-2-222000000000000000004-400-22000000000000-220000000000000000000000000000
χ804-4-4444-22-442-44-4-4-24-2-20422-42-22-4-200-44-2-22200000000000000000-44002-20000000000002-20000000000000000000000000000
χ814-4-444-24-4-4-2-424-424-24-20-2-422-4-2224004-4-2-22200000000000000000-22004-4000000000000-220000000000000000000000000000
χ824-4-444-24-4-4-2-424-424-24-20-2-422-4-222400-44-2-222000000000000000002-200-440000000000002-20000000000000000000000000000
χ834-4-444-2-22-4-2224-42-2-2-210-22-1221-12-2004-411-1-10000003i−3i3i−3i3i−3i00000-2200-220000000000001-13i−3i00000000000000000000000000
χ844-4-444-2-22-4-2224-42-2-2-210-22-1221-12-2004-411-1-1000000−3i3i−3i3i−3i3i00000-2200-220000000000001-1−3i3i00000000000000000000000000
χ854-4-444-2-22-4-2224-42-2-2-210-22-1221-12-200-4411-1-10000003i−3i3i−3i3i−3i000002-2002-2000000000000-11−3i3i00000000000000000000000000
χ864-4-444-2-22-4-2224-42-2-2-210-22-1221-12-200-4411-1-1000000−3i3i−3i3i−3i3i000002-2002-2000000000000-113i−3i00000000000000000000000000
χ874-4-44-244-424-4-4-22-44-2-240-22-4224-42-20000-2-22200000000000000000000000004i−4i00000000000000000000000000000−2i2i0000000
χ884-4-44-244-424-4-4-22-44-2-240-22-4224-42-20000-2-2220000000000000000000000000−4i4i000000000000000000000000000002i−2i0000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-4-8444-88-44-4-4204-4244-2-2-4400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-44-84-84-484-42-4042-44-244-4-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48844-844-4-4-82-4-40-2-4-4-24442400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-444444-4-442220-222-2-2-2-22-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-4-444444-4-442220-222-2-2-2-22-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000
χ968-88-88-4-4484-4-4-8-844-4-42044-2-4-4-224400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-44-4-444442220-2-2-222-22-2-2−4i34i300-111-1002i3−2i32i3−2i300−i3−i3i3i300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-44-4-444442220-2-2-222-22-2-24i3−4i300-111-100−2i32i3−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000
χ998-8-88-48-44484-8-44-8-4-42-40-4-244-2-4442000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-84-4-84-44482-4-40244-24-44-2-4000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-444-444-422202-2-2-2-22-2-220000-1-1110000006i−6i−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-444-444-422202-2-2-2-22-2-220000-1-111000000−6i6i3i−3i3i−3i00000000000000000000000000000000000000000000000000000

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