Finite Group Databasebeta

← Group #13150716

Character table — Group #13150716

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666246612121212336666661212121236666666666612121212121212121212121212122244244444444466121212121212612121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-111111-11-1-11-1-11-111-1-1-1-11111-1-11-11-1
χ61111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1111-1-1-1-111-1-111-11-11
χ71111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11-1-11111-1-111-1-1-11-11
χ81111111111-1-1-1-111-1-11111111111111-1-1-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-1-11-1111-111-1-1-11111-1-1-1-1111-11-1
χ911111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11-11-111111-1-1-1-11-1-111-1-11
χ1011111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-11-11-11111-1-1-1-1-111-1-111-1
χ1111111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-111111-1-11-111-1
χ1211111-1-11111-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-11-1-1-1-11111-111-11-1-11
χ1311111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-1111111-1-111-1-1111-1-1-111-1-111-1-11-11-111-1-1
χ1411111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-1111111-1-1-111-1-1-1-111111-1-111-1-1-11-11-1-111
χ1511111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-1111-1-111-1-1-111-1-111-1-1111-11-1-1-111
χ1611111-1-1111-11-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-111-1-1-1-11111-1-111-1-111-1111-1-1-1-111-1-111-11-1111-1-1
χ172222222222222222222-12-1-1-122-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220202000000-1-1-1-1-1-1-1-100000000
χ182222222222222222222-12-1-1-122-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20-20-20000001111111100000000
χ19222222222222222222-12-1222-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000022022000000000000-1-1-1-1
χ20222222222222222222-12-1222-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1000000000-2-20-2-20000000000001111
χ212222222222-2-2-2-222-2-22-12-1-1-122-1-1-1-1-1-2-211-1-11111-11122-2-2-1-1-1-1111122220-20-2000000-1-11111-1-100000000
χ222222222222-2-2-2-222-2-22-12-1-1-122-1-1-1-1-1-2-211-1-11111-11122-2-2-1-1-1-11111-2-2-2-2020200000011-1-1-1-11100000000
χ232222222222-2-2-2-222-2-2-12-1222-1-12222-111-2-2-1-11111-1-2-2-1-111-1-1-1-111110000000002-202-2000000000000-11-11
χ242222222222-2-2-2-222-2-2-12-1222-1-12222-111-2-2-1-11111-1-2-2-1-111-1-1-1-11111000000000-220-220000000000001-11-1
χ2522222-2-22222-222-2-2-2-22-12-1-1-1221111-122-1-1-1-1-1-1-1-1-111-2-2-2-21111111122-2-20-202000000-1-1-1-1111100000000
χ2622222-2-22222-222-2-2-2-22-12-1-1-1221111-122-1-1-1-1-1-1-1-1-111-2-2-2-211111111-2-222020-20000001111-1-1-1-100000000
χ2722222-2-22222-222-2-2-2-2-12-1222-1-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-21111111111110000000002-20-22000000000000-111-1
χ2822222-2-22222-222-2-2-2-2-12-1222-1-1-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-2111111111111000000000-2202-20000000000001-1-11
χ2922222-2-2222-22-2-2-2-2222-12-1-1-1221111-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-122-2-2020-2000000-1-111-1-11100000000
χ3022222-2-2222-22-2-2-2-2222-12-1-1-1221111-1-2-211-1-11111-1-1-1-2-2221111-1-1-1-1-2-2220-20200000011-1-111-1-100000000
χ3122222-2-2222-22-2-2-2-222-12-1222-1-1-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-1000000000220-2-2000000000000-1-111
χ3222222-2-2222-22-2-2-2-222-12-1222-1-1-2-2-2-2-111-2-2-1-11111-12211-1-11111-1-1-1-1000000000-2-202200000000000011-1-1
χ332-22-222i−2i2-2-200002i−2i0022-22-2-22-22i2i−2i−2i200002-20000-2002i−2i002i2i−2i−2i00002-22i−2i00000000002-200002i−2i00000000
χ342-22-222i−2i2-2-200002i−2i0022-22-2-22-22i2i−2i−2i200002-20000-2002i−2i002i2i−2i−2i0000-22−2i2i0000000000-220000−2i2i00000000
χ352-22-222i−2i2-2-200002i−2i002-1-2-1112-2−i−iii-100−i3i3-11−i3−i3i3i313−32i−2i00−i−iii33−3−32-22i−2i0000000000-11−i3i33−3−ii00000000
χ362-22-222i−2i2-2-200002i−2i002-1-2-1112-2−i−iii-100−i3i3-11−i3−i3i3i313−32i−2i00−i−iii33−3−3-22−2i2i00000000001-1i3−i3−33i−i00000000
χ372-22-222i−2i2-2-200002i−2i002-1-2-1112-2−i−iii-100i3−i3-11i3i3−i3−i31−332i−2i00−i−iii−3−3332-22i−2i0000000000-11i3−i3−33−ii00000000
χ382-22-222i−2i2-2-200002i−2i002-1-2-1112-2−i−iii-100i3−i3-11i3i3−i3−i31−332i−2i00−i−iii−3−333-22−2i2i00000000001-1−i3i33−3i−i00000000
χ392-22-22−2i2i2-2-20000−2i2i0022-22-2-22-2−2i−2i2i2i200002-20000-200−2i2i00−2i−2i2i2i00002-2−2i2i00000000002-20000−2i2i00000000
χ402-22-22−2i2i2-2-20000−2i2i0022-22-2-22-2−2i−2i2i2i200002-20000-200−2i2i00−2i−2i2i2i0000-222i−2i0000000000-2200002i−2i00000000
χ412-22-22−2i2i2-2-20000−2i2i002-1-2-1112-2ii−i−i-100−i3i3-11−i3−i3i3i31−33−2i2i00ii−i−i−3−3332-2−2i2i0000000000-11−i3i3−33i−i00000000
χ422-22-22−2i2i2-2-20000−2i2i002-1-2-1112-2ii−i−i-100−i3i3-11−i3−i3i3i31−33−2i2i00ii−i−i−3−333-222i−2i00000000001-1i3−i33−3−ii00000000
χ432-22-22−2i2i2-2-20000−2i2i002-1-2-1112-2ii−i−i-100i3−i3-11i3i3−i3−i313−3−2i2i00ii−i−i33−3−32-2−2i2i0000000000-11i3−i33−3i−i00000000
χ442-22-22−2i2i2-2-20000−2i2i002-1-2-1112-2ii−i−i-100i3−i3-11i3i3−i3−i313−3−2i2i00ii−i−i33−3−3-222i−2i00000000001-1−i3i3−33−ii00000000
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ464444444444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000000000
χ4744444-4-44444-444-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ4844444-4-4444-44-4-4-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4944-4-4400-44-400000000444-44-4-4-4000040000-440000-400000000000000000000000000000000000000000000
χ5044-4-4400-44-4000000004-242-22-4-423−2323−23-200002-20000200000023−2323−230000000000000000000000000000000000
χ5144-4-4400-44-4000000004-242-22-4-4−2323−2323-200002-200002000000−2323−23230000000000000000000000000000000000
χ5244-4-4400-44-400000000-24-2-44-4220000-2−2i32i3002-2−2i32i3−2i32i3200000000000000000000000000000000000000000000
χ5344-4-4400-44-400000000-24-2-44-4220000-22i3−2i3002-22i3−2i32i3−2i3200000000000000000000000000000000000000000000
χ5444-4-4400-44-400000000-2-2-22-222223−2323−231−2i32i300-11i3−i3i3−i3-1000000−33−333i−3i3i−3i000000000000000000000000000000
χ5544-4-4400-44-400000000-2-2-22-222223−2323−2312i3−2i300-11−i3i3−i3i3-1000000−33−33−3i3i−3i3i000000000000000000000000000000
χ5644-4-4400-44-400000000-2-2-22-2222−2323−23231−2i32i300-11i3−i3i3−i3-10000003−33−3−3i3i−3i3i000000000000000000000000000000
χ5744-4-4400-44-400000000-2-2-22-2222−2323−232312i3−2i300-11−i3i3−i3i3-10000003−33−33i−3i3i−3i000000000000000000000000000000
χ584-44-444i−4i4-4-400004i−4i00-2424-4-4-224i4i−4i−4i-20000-220000200−2i2i00−2i−2i2i2i0000000000000000000000000000000000
χ594-44-444i−4i4-4-400004i−4i00-2-22-222-22−2i−2i2i2i100−2i32i31-1i3i3−i3−i3-123−23−2i2i00ii−i−i−3−333000000000000000000000000000000
χ604-44-444i−4i4-4-400004i−4i00-2-22-222-22−2i−2i2i2i1002i3−2i31-1−i3−i3i3i3-1−2323−2i2i00ii−i−i33−3−3000000000000000000000000000000
χ614-44-44−4i4i4-4-40000−4i4i00-2424-4-4-22−4i−4i4i4i-20000-2200002002i−2i002i2i−2i−2i0000000000000000000000000000000000
χ624-44-44−4i4i4-4-40000−4i4i00-2-22-222-222i2i−2i−2i100−2i32i31-1i3i3−i3−i3-1−23232i−2i00−i−iii33−3−3000000000000000000000000000000
χ634-44-44−4i4i4-4-40000−4i4i00-2-22-222-222i2i−2i−2i1002i3−2i31-1−i3−i3i3i3-123−232i−2i00−i−iii−3−333000000000000000000000000000000
χ644-4-44400-4-440000000044-4-4-44-44000040000-4-40000400000000000000000000000000000000000000000000
χ654-4-44400-4-44000000004-2-422-2-44−2i32i32i3−2i3-20000220000-2000000−2i32i32i3−2i30000000000000000000000000000000000
χ664-4-44400-4-44000000004-2-422-2-442i3−2i3−2i32i3-20000220000-20000002i3−2i3−2i32i30000000000000000000000000000000000
χ674-4-44400-4-4400000000-242-4-442-20000-20000220000-20000−2i32i30000−2i32i32i3−2i3000000000000000000000000000000
χ684-4-44400-4-4400000000-242-4-442-20000-20000220000-200002i3−2i300002i3−2i3−2i32i3000000000000000000000000000000
χ694-4-44400-4-4400000000-2-2222-22-2−2i32i32i3−2i310000-1-13-3-3310000−2i32i3i3−i3−i3i3i3−i3−i3i3000000000000000000000000000000
χ704-4-44400-4-4400000000-2-2222-22-2−2i32i32i3−2i310000-1-1-333-3100002i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000
χ714-4-44400-4-4400000000-2-2222-22-22i3−2i3−2i32i310000-1-13-3-33100002i3−2i3−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000
χ724-4-44400-4-4400000000-2-2222-22-22i3−2i3−2i32i310000-1-1-333-310000−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000
χ736666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000202020020000000000-1-1-1-10000
χ746666-366-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000-20-20-200-2000000000011110000
χ756666-366-3-3-3-6-633-3-3330000000000000000000000000000000000000000002020-200-20000000000-1-1110000
χ766666-366-3-3-3-6-633-3-333000000000000000000000000000000000000000000-20-202002000000000011-1-10000
χ776666-3-6-6-3-3-36-6-3-3333300000000000000000000000000000000000000000020-20-20020000000000-111-10000
χ786666-3-6-6-3-3-36-6-3-33333000000000000000000000000000000000000000000-2020200-200000000001-1-110000
χ796666-3-6-6-3-3-3-663333-3-300000000000000000000000000000000000000000020-20200-20000000000-11-110000
χ806666-3-6-6-3-3-3-663333-3-3000000000000000000000000000000000000000000-2020-200200000000001-11-10000
χ811212-12-12-6006-6600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-12-6006-66000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-12-612i−12i-6660000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-6−12i12i-66600006i−6i0000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-600−6i36i3000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-6006i3−6i3000000000000000000000000000000000000000000000000000000000000000000000000

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