Finite Group Databasebeta

← Group #13168635

Character table — Group #13168635

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666663334666666666121236661212121212121212121212122224446666121212124444446666666666121212121212121212122246612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-111111111111-1-1-111-1-1-1-1-1-11-1-1-1-111-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1111-111-1-11111-1111-1-111111-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111-111
χ511111111111111111111111111111111111111111111111-1-11111-1-1111111-1-111-1-1-11-1-111-1-1-1-11111111111-11-1-1-1-1-1-1-1111-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1-1-1-11-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-11-1-1-1-111-1-1-1111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11111-1-111-1-111-1-1-111-11111-1-1-11-1-1-1-111-1-11-1111-1-1-1-111-11-11
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111-1-1-1-1-1-1-1-111-111-11111-1-1-1-111-1-1-1-111-111-1-111-1-1-1-1111-1
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-1111111-1-1-1-1-1-11-1-1-111-1-111-1-11111-1-111-111-1-111-1-11-11-1
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-111-1-1111111-1-11-1-1-111-1-11-11111-1-111-1-1-1-1-1111111-1-1-11
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-11111111111-1111-1-111-11-1-1-1-111-1-1-1-1-1-1-1111111-1-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-111-1-1-1-111-1111-1-111-1-111-1-1-1-11111-111-1-111-1-11-1-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-11111-1-1-1-1111-1-11-1-1-1-11111-1-11111-1-1-111-1-111-1-1-1-111-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-1-1-111-1-11-1-11-1-1-1-1111-11111-1-1111-1111-1-1-1-111-111-1
χ17222222-12-122-12-122-12-12-12-1-1-12-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200222200002200002220-1-100-1-1-1-10-1-1200-1-1-1-1200-1-1-1-100000000
χ18222222-12-122-12-122-12-12-12-1-1-12-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-2-2220000-2-20000-2-220-1-100-1-1-1-1011-2001111-200111100000000
χ19222222-12-122-12-122-12-12-12-1-1-12-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-20022-2-20000220000-2-2-20110011110-1-1200-1-1-1-1-200111100000000
χ20222222-12-122-12-122-12-12-12-1-1-12-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-2-2-20000-2-2000022-2011001111011-2001111200-1-1-1-100000000
χ21222222-12-122-12-122-12-1-2-12-1-1-12-12-111-1-1-1-1-2-2-2-2111111112-2002-2220000220000-2-2-20-1100-1-1110-11-200-1-111200-1-11100000000
χ22222222-12-122-12-122-12-1-2-12-1-1-12-12-111-1-1-1-1-2-2-2-2111111112-200-22220000-2-2000022-20-1100-1-11101-120011-1-1-20011-1-100000000
χ23222222-12-122-12-122-12-1-2-12-1-1-12-12-111-1-1-1-1-2-2-2-211111111-22002-2-2-2000022000022201-10011-1-10-11-200-1-111-20011-1-100000000
χ24222222-12-122-12-122-12-1-2-12-1-1-12-12-111-1-1-1-1-2-2-2-211111111-2200-22-2-20000-2-20000-2-2201-10011-1-101-120011-1-1200-1-11100000000
χ2522222-1222-1-12222-1-1-122-1-122-1-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-100222200-1-122-1-10022000200-1-10000-122-1-1-1-1-1-1-1020000000-1-1-1000
χ2622222-1222-1-12222-1-1-122-1-122-1-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-10022-2-200-1-1221100-2-2000200-1-10000-1-2-21-1-111110-20000000111000
χ2722222-1222-1-12222-1-1-122-1-122-1-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-100-2-2220011-2-2-1-100-2-2000-200110000122-111-1-1-1-10-20000000111000
χ2822222-1222-1-12222-1-1-122-1-122-1-12-1-122-1-1-1-1-12-1-122-1-1-1-1-1-100-2-2-2-20011-2-2110022000-2001100001-2-21111111020000000-1-1-1000
χ2922222-1222-1-12222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-211-2-2111111002-22-200-1-1-2-2-1-10022000200-1-1000012-2111-1-1110-20000000-1-11000
χ3022222-1222-1-12222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-211-2-2111111002-2-2200-1-1-2-21100-2-2000200-1-100001-22-11111-1-102000000011-1000
χ3122222-1222-1-12222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-211-2-211111100-222-2001122-1-100-2-2000-200110000-12-21-1-1-1-11102000000011-1000
χ3222222-1222-1-12222-1-1-12-2-1-122-1-12-1-1-2-2-1-1-1-11-211-2-211111100-22-22001122110022000-200110000-1-22-1-1-111-1-10-20000000-1-11000
χ332222-122-12222-12-122-1-122-1-1-12-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1222200-1-122-1-100220000-1-122-1-1-1-1-1-12000-1-100000020000-1-1000-100
χ342222-122-12222-12-122-1-122-1-1-12-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-122-2-200-1-1-2-21100-2-20000-112211-1-1-1-1-200011000000-2000011000100
χ352222-122-12222-12-122-1-122-1-1-12-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-2-222001122-1-100-2-200001-1-2-2-1-111112000-1-1000000-2000011000100
χ362222-122-12222-12-122-1-122-1-1-12-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-1-2-2-2-20011-2-2110022000011-2-2111111-20001100000020000-1-1000-100
χ372222-122-12222-12-122-1-1-22-1-1-12-1-1-12-2-2-1-1-1-1-211111-2-211112-22-200-1-1221100-2-200001-12-2-1-1-1-111-2000110000002000011000-100
χ382222-122-12222-12-122-1-1-22-1-1-12-1-1-12-2-2-1-1-1-1-211111-2-211112-2-2200-1-1-2-2-1-100220000112-211-1-1112000-1-1000000-20000-1-1000100
χ392222-122-12222-12-122-1-1-22-1-1-12-1-1-12-2-2-1-1-1-1-211111-2-21111-222-20011221100220000-1-1-22-1-111-1-1-200011000000-20000-1-1000100
χ402222-122-12222-12-122-1-1-22-1-1-12-1-1-12-2-2-1-1-1-1-211111-2-21111-22-220011-2-2-1-100-2-20000-11-221111-1-12000-1-10000002000011000-100
χ4122-2-2222-22-22-2-2-22-222202-22-2-2-2-22-20022-2-2000000000000000000000000002-22i−2i2i−2i00000000000000000000000002i−2i2-22i−2i0000
χ4222-2-2222-22-22-2-2-22-222202-22-2-2-2-22-20022-2-2000000000000000000000000002-2−2i2i−2i2i0000000000000000000000000−2i2i2-2−2i2i0000
χ4322-2-2222-22-22-2-2-22-222202-22-2-2-2-22-20022-2-200000000000000000000000000-222i−2i−2i2i0000000000000000000000000−2i2i-222i−2i0000
χ4422-2-2222-22-22-2-2-22-222202-22-2-2-2-22-20022-2-200000000000000000000000000-22−2i2i2i−2i00000000000000000000000002i−2i-22−2i2i0000
χ4544444-2-24-2-2-2-24-24-21-2-241-2-2-21-2-2-21-2-21111-24-2-2-2-2111111000044000000-2-200000000000000000-2-2-2001111000000000000000
χ4644444-2-24-2-2-2-24-24-21-2-241-2-2-21-2-2-21-2-21111-24-2-2-2-21111110000-4-4000000220000000000000000022200-1-1-1-1000000000000000
χ4744444-2-24-2-2-2-24-24-21-2-2-41-2-2-21-2-2-212211112-42222-1-1-1-1-1-100004-4000000-2-200000000000000000-2220011-1-1000000000000000
χ4844444-2-24-2-2-2-24-24-21-2-2-41-2-2-21-2-2-212211112-42222-1-1-1-1-1-10000-4400000022000000000000000002-2-200-1-111000000000000000
χ494444-24-2-2-244-2-2-2-24-2-214-2-211-2-21-2-2-2-211114-2-2-211-2-21111440000-2-2000000000000-20-2-20011110000000000000000000000000
χ504444-24-2-2-244-2-2-2-24-2-214-2-211-2-21-2-2-2-211114-2-2-211-2-21111-4-4000022000000000000202200-1-1-1-10000000000000000000000000
χ514444-24-2-2-244-2-2-2-24-2-21-4-2-211-2-21-2-2221111-4222-1-122-1-1-1-14-40000-2-200000000000020-220011-1-10000000000000000000000000
χ524444-24-2-2-244-2-2-2-24-2-21-4-2-211-2-21-2-2221111-4222-1-122-1-1-1-1-44000022000000000000-202-200-1-1110000000000000000000000000
χ534444-2-24-24-2-24-24-2-2-21-24-21-2-2-21-21-2441111-2-211-2-2-2-2111100440000-2-2-2-2000000000-200110000-2000110000000000000000000
χ544444-2-24-24-2-24-24-2-2-21-24-21-2-2-21-21-2441111-2-211-2-2-2-2111100-4-400002222000000000200-1-100002000-1-10000000000000000000
χ554444-2-24-24-2-24-24-2-2-21-2-4-21-2-2-21-21-2-4-4111122-1-12222-1-1-1-1004-40000-2-222000000000-2001100002000-1-10000000000000000000
χ564444-2-24-24-2-24-24-2-2-21-2-4-21-2-2-21-21-2-4-4111122-1-12222-1-1-1-100-44000022-2-2000000000200-1-10000-2000110000000000000000000
χ5744-4-444-2-4-2-442-424-4-24-20-2-4-222-424200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ5844-4-444-2-4-2-442-424-4-24-20-2-4-222-424200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ5944-4-44-24-442-2-4-4-442-2-240-224-422-4-2200-2-22200000000000000000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ6044-4-44-24-442-2-4-4-442-2-240-224-422-4-2200-2-2220000000000000000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ6144-4-4-24424-44-42-4-2-44-2-2042-22-422-2-400-2-222000000000000000000000000004-40000000000000000000000000000000-22000000
χ6244-4-4-24424-44-42-4-2-44-2-2042-22-422-2-400-2-22200000000000000000000000000-4400000000000000000000000000000002-2000000
χ634-44-44444-4-4-44-4-4-444440-44-44-4-4-4-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ644-44-444-242-4-4-2-42-44-24-20242-22-42-4-200-22-220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ654-44-444-242-4-4-2-42-44-24-20242-22-42-4-200-22-2200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ664-44-44-244-4224-4-4-4-2-2-2402-2-4422-42-200-22-2200000000000000000000−2i32i300000000000000−2i32i300000000000000000000000000000
χ674-44-44-244-4224-4-4-4-2-2-2402-2-4422-42-200-22-22000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000000000
χ684-44-4-244-2-4-4-442-4244-2-20-4-22-2-4222400-22-22000000000000000000000023−23000000000000000000000023−230000000000000000000
χ694-44-4-244-2-4-4-442-4244-2-20-4-22-2-4222400-22-220000000000000000000000−23230000000000000000000000−23230000000000000000000
χ704-44-4-2-24-2-42242-42-2-21-20212-22-12-1-2001-11-1003i−3i00003i3i−3i−3i00000000−2i32i323−23000000000000i3−i300000000−330000000000000000000
χ714-44-4-2-24-2-42242-42-2-21-20212-22-12-1-2001-11-1003i−3i00003i3i−3i−3i000000002i3−2i3−2323000000000000−i3i3000000003−30000000000000000000
χ724-44-4-2-24-2-42242-42-2-21-20212-22-12-1-2001-11-100−3i3i0000−3i−3i3i3i00000000−2i32i3−2323000000000000i3−i3000000003−30000000000000000000
χ734-44-4-2-24-2-42242-42-2-21-20212-22-12-1-2001-11-100−3i3i0000−3i−3i3i3i000000002i3−2i323−23000000000000−i3i300000000−330000000000000000000
χ744-4-44444-4-44-4-444-4-44440-4-4-4-4444-4-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-424-424-2-4-4-24-202-422-24-2-42−2i32i3-222-20000−2i32i3−2i32i3−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ764-4-4444-2-424-424-2-4-4-24-202-422-24-2-422i3−2i3-222-200002i3−2i32i3−2i32i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ774-4-444-24-4-4-22-444-42-2-24022-4-4-2-242200-222-200000000000000000000000023−23000000000000000000000023−2300000000000000000
χ784-4-444-24-4-4-22-444-42-2-24022-4-4-2-242200-222-2000000000000000000000000−23230000000000000000000000−232300000000000000000
χ794-4-444-2-2-42-2224-2-421-2-20-12221-2-22-1−2i32i31-1-110000−2i32i3i3−i3i3−i3i3−i300000000000023−230000000000000000000000−333i−3i000000000000000
χ804-4-444-2-2-42-2224-2-421-2-20-12221-2-22-1−2i32i31-1-110000−2i32i3i3−i3i3−i3i3−i3000000000000−232300000000000000000000003−3−3i3i000000000000000
χ814-4-444-2-2-42-2224-2-421-2-20-12221-2-22-12i3−2i31-1-1100002i3−2i3−i3i3−i3i3−i3i300000000000023−230000000000000000000000−33−3i3i000000000000000
χ824-4-444-2-2-42-2224-2-421-2-20-12221-2-22-12i3−2i31-1-1100002i3−2i3−i3i3−i3i3−i3i3000000000000−232300000000000000000000003−33i−3i000000000000000
χ834-4-44-2442-44-4-4-242-44-2-20-42224-2-22-400-222-2000000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000000000
χ844-4-44-2442-44-4-4-242-44-2-20-42224-2-22-400-222-20000000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000000000
χ854-4-44-24-2224-42-2-22-4-2-21022-1-1-2-2122−2i32i31-1-110000i3−i3−2i32i3i3−i3i3−i3000000−2i32i3000000000000000000i3−i33-30000000000000000000000000
χ864-4-44-24-2224-42-2-22-4-2-21022-1-1-2-2122−2i32i31-1-110000i3−i3−2i32i3i3−i3i3−i30000002i3−2i3000000000000000000−i3i3-330000000000000000000000000
χ874-4-44-24-2224-42-2-22-4-2-21022-1-1-2-21222i3−2i31-1-110000−i3i32i3−2i3−i3i3−i3i3000000−2i32i3000000000000000000i3−i3-330000000000000000000000000
χ884-4-44-24-2224-42-2-22-4-2-21022-1-1-2-21222i3−2i31-1-110000−i3i32i3−2i3−i3i3−i3i30000002i3−2i3000000000000000000−i3i33-30000000000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-8-44-44-84842-4-4024-44-244-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-44-4-88444-4-8-4-420-442-244-2-440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48484-4-84-8-44-42-40-4-2-444-24240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-44-4444-4422202-22-2-2-2-22-200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-44-4444-4422202-22-2-2-2-22-200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000
χ968-88-88-4-48444-4-84-8-42-4-40-2-44-4-24442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-48-4-44-8-8-44448-4-4204-4-2244-24-4002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4444-4444-42220-22-22-2-2-2-2200-11-11006i−6i0000−3i−3i3i3i0000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-4444-4444-42220-22-22-2-2-2-2200-11-1100−6i6i00003i3i−3i−3i0000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8-44-8-4844-42-404-244-42-4-24002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-444-4-4442220-2-2-2-2222-2-2−4i34i3-111-100002i3−2i32i3−2i3−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-444-4-4442220-2-2-2-2222-2-24i3−4i3-111-10000−2i32i3−2i32i3i3−i3i3−i30000000000000000000000000000000000000000000000000000000

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