Finite Group Databasebeta

← Group #13149541

Character table — Group #13149541

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121222224444446666121212121212121222444446666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-1-1-111-1-1-1-111-1-1-1-11-1-11
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-11-11-1-1111-1-111-1-1-1-1-1-1-1-1-111-1
χ51111111111-1-11111111111-1-11111-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-11-1-111-1111111-1-11111-1-1-1-1-1-1
χ61111111111-1-11111111111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1111-11-1-1-1-1-1-1-1-1-1-111-1-11111
χ71111111111-1-11111111111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-111-1-111-1-11111-1-111-111-1
χ81111111111-1-11111111111-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-111-1-11111-1-1-1-1111-1-11
χ911111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1111111-1-11111111-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-11-11
χ1011111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-111-1-111-1-1-1-111111-111-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-11-11-1
χ1111111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111-1-1-1-1-111-11-111111-1-1-1-1-1-11111-1-111
χ1211111-1-11111-1-1-1111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-11-1-1111-1-1-1-1-111-1-111111111-1-1
χ1311111-1-1111-11-1-111111111-111111-1-1-1-1-1-1111111-1-111111111-11-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-1-1-1111-11-1
χ1411111-1-1111-11-1-111111111-111111-1-1-1-1-1-11111-1-1-1-111-1-11111-11-1-1-1-111-1111-11-111-1-1-1-1-1-111-1-111-11-11
χ1511111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-11111-111-1-11111-1-111-1-111-1-111-1-1
χ1611111-1-1111-11-1-111111111-111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-11-1-1-1-111-1-11-1111-1-1-1-111111111-1-1-1-111
χ17222222222222222-12-1-12-1222-1-1-1-122-1-1222200220000000000-1-1-1-1-1-1-1-1202002000-1-10000-1-10000-100-1
χ18222222222222222-12-1-12-1222-1-1-1-122-1-1222200-2-20000000000-1-1-1-1-1-1-1-1-20-200-20001100001100001001
χ1922222222222222-12-122-12-122-1-1-1-1-1-122-1-1-1-12200222200-1-1-1-122-1-1-1-1-1-10000200000000-1-100-1-1-1-10000
χ2022222222222222-12-122-12-122-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-200111122-1-1-1-1-1-10000-200000000110011110000
χ212222222222-2-2222-12-1-12-12-2-2-1-1-1-1-2-2-1-122-2-2002200000000001111-1-111-20-2002000-1-10000-1-100001001
χ222222222222-2-2222-12-1-12-12-2-2-1-1-1-1-2-2-1-122-2-200-2-200000000001111-1-11120200-2000110000110000-100-1
χ232222222222-2-222-12-122-12-1-2-2-1-1-1-11122-1-1112200-2-2-2-200-1-1-1-1-2-211-1-11100002000000001100-1-1110000
χ242222222222-2-222-12-122-12-1-2-2-1-1-1-11122-1-111-2-2002222001111-2-211-1-1110000-200000000-1-10011-1-10000
χ2522222-2-22222-2-2-22-12-1-12-122-2-1-1-1-12211-2-2-2-200220000000000-11-1-11111-20200-2000-1-10000110000100-1
χ2622222-2-22222-2-2-22-12-1-12-122-2-1-1-1-12211-2-2-2-200-2-20000000000-11-1-1111120-2002000110000-1-10000-1001
χ2722222-2-22222-2-2-2-12-122-12-12-2-1-1-1-1-1-1-2-21111220022-2-200-1-1-1-12-2-1-111110000-200000000-1-10011110000
χ2822222-2-22222-2-2-2-12-122-12-12-2-1-1-1-1-1-1-2-21111-2-200-2-2220011112-2-1-1111100002000000001100-1-1-1-10000
χ2922222-2-2222-22-2-22-12-1-12-12-22-1-1-1-1-2-211-2-222002200000000001-11111-1-120-200-2000-1-10000110000-1001
χ3022222-2-2222-22-2-22-12-1-12-12-22-1-1-1-1-2-211-2-22200-2-200000000001-11111-1-1-202002000110000-1-10000100-1
χ3122222-2-2222-22-2-2-12-122-12-1-22-1-1-1-111-2-211-1-12200-2-22200-1-1-1-1-221111-1-10000-200000000110011-1-10000
χ3222222-2-2222-22-2-2-12-122-12-1-22-1-1-1-111-2-211-1-1-2-20022-2-2001111-221111-1-10000200000000-1-100-1-1110000
χ332-22-222i−2i-22-2002i−2i22-22-22-2-2002-22-2002i−2i2i−2i0000002-22i−2i00000000002i−2i0000000000000002-200002i−2i0000
χ342-22-222i−2i-22-2002i−2i22-22-22-2-2002-22-2002i−2i2i−2i000000-22−2i2i00000000002i−2i000000000000000-220000−2i2i0000
χ352-22-222i−2i-22-2002i−2i-1212-2-1-2100-11-11−i3i32i−2i−ii3−300002-22i−2i00−i3−i3i3i300−i3i3−ii3−30000000000000-11003−3−ii0000
χ362-22-222i−2i-22-2002i−2i-1212-2-1-2100-11-11−i3i32i−2i−ii3−30000-22−2i2i00i3i3−i3−i300−i3i3−ii3−300000000000001-100−33i−i0000
χ372-22-222i−2i-22-2002i−2i-1212-2-1-2100-11-11i3−i32i−2i−ii−3300002-22i−2i00i3i3−i3−i300i3−i3−ii−330000000000000-1100−33−ii0000
χ382-22-222i−2i-22-2002i−2i-1212-2-1-2100-11-11i3−i32i−2i−ii−330000-22−2i2i00−i3−i3i3i300i3−i3−ii−3300000000000001-1003−3i−i0000
χ392-22-22−2i2i-22-200−2i2i22-22-22-2-2002-22-200−2i2i−2i2i0000002-2−2i2i0000000000−2i2i0000000000000002-20000−2i2i0000
χ402-22-22−2i2i-22-200−2i2i22-22-22-2-2002-22-200−2i2i−2i2i000000-222i−2i0000000000−2i2i000000000000000-2200002i−2i0000
χ412-22-22−2i2i-22-200−2i2i-1212-2-1-2100-11-11−i3i3−2i2ii−i−3300002-2−2i2i00−i3−i3i3i300−i3i3i−i−330000000000000-1100−33i−i0000
χ422-22-22−2i2i-22-200−2i2i-1212-2-1-2100-11-11−i3i3−2i2ii−i−330000-222i−2i00i3i3−i3−i300−i3i3i−i−3300000000000001-1003−3−ii0000
χ432-22-22−2i2i-22-200−2i2i-1212-2-1-2100-11-11i3−i3−2i2ii−i3−300002-2−2i2i00i3i3−i3−i300i3−i3i−i3−30000000000000-11003−3i−i0000
χ442-22-22−2i2i-22-200−2i2i-1212-2-1-2100-11-11i3−i3−2i2ii−i3−30000-222i−2i00−i3−i3i3i300i3−i3i−i3−300000000000001-100−33−ii0000
χ452-2-22200-2-22000022-2-2-2-222002-2-22000000002-22-200002-22-22-2000000000000000002-22-2000000000000
χ462-2-22200-2-22000022-2-2-2-222002-2-22000000002-2-220000-222-22-200000000000000000-22-22000000000000
χ472-2-22200-2-22000022-2-2-2-222002-2-2200000000-222-20000-22-22-22000000000000000002-2-22000000000000
χ482-2-22200-2-22000022-2-2-2-222002-2-2200000000-22-2200002-2-22-2200000000000000000-222-2000000000000
χ4944444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-4111122-2-2-2-2220000000000000022-1-111-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41111-2-222222200000000000000-2211-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-441111222222-2-2000000000000002-2-1-1-1-1110000000000000000000000000
χ5344-4-44004-4-40000444-44-4-4-40044-4-40000000000000000000000000000000000000000000000000000000
χ5444-4-44004-4-400004-242-2-42-400-2-22200000000000000000000000000000000000000000000023−2300000000
χ5544-4-44004-4-400004-242-2-42-400-2-222000000000000000000000000000000000000000000000−232300000000
χ5644-4-44004-4-40000-24-2-442-4200-2-222000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ5744-4-44004-4-40000-24-2-442-4200-2-2220000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ584-44-444i−4i-44-4004i−4i4-2-4-2242-400-22-2200−2i2i4i−4i00000000000000000000−2i2i000000000000000000000000000
χ594-44-444i−4i-44-4004i−4i-2-22-22-222001-11-1−2i32i3−2i2i−2i2i23−230000000000000000i3−i3i−i−330000000000000000000000000
χ604-44-444i−4i-44-4004i−4i-2-22-22-222001-11-12i3−2i3−2i2i−2i2i−23230000000000000000−i3i3i−i3−30000000000000000000000000
χ614-44-44−4i4i-44-400−4i4i4-2-4-2242-400-22-22002i−2i−4i4i000000000000000000002i−2i000000000000000000000000000
χ624-44-44−4i4i-44-400−4i4i-2-22-22-222001-11-1−2i32i32i−2i2i−2i−23230000000000000000i3−i3−ii3−30000000000000000000000000
χ634-44-44−4i4i-44-400−4i4i-2-22-22-222001-11-12i3−2i32i−2i2i−2i23−230000000000000000−i3i3−ii−330000000000000000000000000
χ644-4-44400-4-4400004-2-422-4-2400-222-200000000004-4000000000000000000000000000-2200000000000000
χ654-4-44400-4-4400004-2-422-4-2400-222-20000000000-440000000000000000000000000002-200000000000000
χ664-4-44400-4-440000-242-4-424-200-222-2000000004-400000000-22-22000000000000000000000000000000000
χ674-4-44400-4-440000-242-4-424-200-222-200000000-44000000002-22-2000000000000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-300000000000000000000220000000000000202002-1-100-1-1000000000-1-10
χ696666-366-3-3-366-3-300000000-3-300000000000000000000-2-20000000000000-20-200-2110011000000000110
χ706666-366-3-3-3-6-6-3-300000000330000000000000000000022000000000000020-200-2-1-100-1-1000000000110
χ716666-366-3-3-3-6-6-3-3000000003300000000000000000000-2-20000000000000-202002110011000000000-1-10
χ726666-3-6-6-3-3-36-63300000000-3300000000000000000000220000000000000-20200-21100-1-1000000000-110
χ736666-3-6-6-3-3-36-63300000000-3300000000000000000000-2-2000000000000020-2002-1-100110000000001-10
χ746666-3-6-6-3-3-3-6633000000003-300000000000000000000220000000000000-20-20021100-1-10000000001-10
χ756666-3-6-6-3-3-3-6633000000003-300000000000000000000-2-2000000000000020200-2-1-10011000000000-110
χ7688-8-88008-8-80000-4-4-44-44440022-2-20000000000000000000000000000000000000000000000000000000
χ778-8-88800-8-880000-4-44444-4-4002-2-220000000000000000000000000000000000000000000000000000000
χ781212-12-12-600-6660000000000000000000000000000000000000000000000000000000−2i32i30000000000000000
χ791212-12-12-600-66600000000000000000000000000000000000000000000000000000002i3−2i30000000000000000
χ8012-1212-12-612i−12i6-6600−6i6i000000000000000000000000000000000000000000000000000000000000000000000
χ8112-1212-12-6−12i12i6-66006i−6i000000000000000000000000000000000000000000000000000000000000000000000
χ8212-12-1212-60066-600000000000000000000000000000000004-400000000000000000000000-22000000000000
χ8312-12-1212-60066-60000000000000000000000000000000000-44000000000000000000000002-2000000000000

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