Finite Group Databasebeta

← Group #13140226

Character table — Group #13140226

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ922222222222222222222222-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000022000022000000000000-1-1-1-10000-1-1-1-1
χ1022222222222222222222222-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000-2-2000000000000111100001111
χ112222222222222222222222-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100220000220000000000-1-1-1-10000-1-1-1-10000
χ122222222222222222222222-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-20000-2-200000000001111000011110000
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000220000-2-2000000000000-1-1-1-100001111
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-200002200000000000011110000-1-1-1-1
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-11111-2-2-2-21111111100220000-2-20000000000-1-1-1-1000011110000
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-11111-2-2-2-21111111100-2-2000022000000000011110000-1-1-1-10000
χ17222-22-2-2-22222-2-2-2-200000022222-2-222-2-2-2-22-2-22222-2-2-2-2000000000000000000002-200000000000000000022-2-200000000
χ18222-22-2-2-22222-2-2-2-200000022222-2-222-2-2-2-22-2-22222-2-2-2-200000000000000000000-22000000000000000000-2-22200000000
χ19222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-1-21-1-1-1-11111000033−3−33333−3−3−3−300002-2000000000000000000-1-111000033−3−3
χ20222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-1-21-1-1-1-11111000033−3−33333−3−3−3−30000-2200000000000000000011-1-10000−3−333
χ21222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-1-21-1-1-1-111110000−3−333−3−3−3−3333300002-2000000000000000000-1-1110000−3−333
χ22222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-1-21-1-1-1-111110000−3−333−3−3−3−333330000-2200000000000000000011-1-1000033−3−3
χ2322-22-22-2-222-2-222-2-2000000222-2-22-22-222-22-2-2-222-2-222-2-20000000000000000002-2000000000000000022-2-2000000000000
χ2422-22-22-2-222-2-222-2-2000000222-2-22-22-222-22-2-2-222-2-222-2-2000000000000000000-220000000000000000-2-222000000000000
χ2522-22-22-2-222-2-222-2-2000000-12-111-112-222-2-1-21-2-1-111-1-11133−3−3000033−3−333−3−3002-20000000000000000-1-111000033−3−30000
χ2622-22-22-2-222-2-222-2-2000000-12-111-112-222-2-1-21-2-1-111-1-11133−3−3000033−3−333−3−300-22000000000000000011-1-10000−3−3330000
χ2722-22-22-2-222-2-222-2-2000000-12-111-112-222-2-1-21-2-1-111-1-111−3−3330000−3−333−3−333002-20000000000000000-1-1110000−3−3330000
χ2822-22-22-2-222-2-222-2-2000000-12-111-112-222-2-1-21-2-1-111-1-111−3−3330000−3−333−3−33300-22000000000000000011-1-1000033−3−30000
χ2922-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-22-2-22222-2-2-2-22200000000000000000000002-20000000022-2-20000000000000000
χ3022-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-22-2-22222-2-2-2-2220000000000000000000000-2200000000-2-2220000000000000000
χ312-222-2-22-22-22-22-22-200000022-22-222-222-22-2-2-2-22-22-22-22-200000000000000002-2000000000022-2-200000000000000000000
χ322-222-2-22-22-22-22-22-200000022-22-222-222-22-2-2-2-22-22-22-22-20000000000000000-220000000000-2-22200000000000000000000
χ332-22-2-22-222-22-2-22-2200000022-22-2-2-2-22-22-22-2222-22-2-22-220000000000000000000000002-20000000000000000002-22-20000
χ342-22-2-22-222-22-2-22-2200000022-22-2-2-2-22-22-22-2222-22-2-22-22000000000000000000000000-22000000000000000000-22-220000
χ352-22-2-22-222-22-2-22-22000000-121-1111-22-22-2-1-2-12-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3000000002-20000000000−i3i3−i3i30000-11-110000
χ362-22-2-22-222-22-2-22-22000000-121-1111-22-22-2-1-2-12-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300000000-220000000000i3−i3i3−i300001-11-10000
χ372-22-2-22-222-22-2-22-22000000-121-1111-22-22-2-1-2-12-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3000000002-20000000000i3−i3i3−i30000-11-110000
χ382-22-2-22-222-22-2-22-22000000-121-1111-22-22-2-1-2-12-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300000000-220000000000−i3i3−i3i300001-11-10000
χ392-2-222-2-222-2-222-2-2200000022-2-222-2-2-22-2-2-22222-2-222-2-22000000000000000000000000002-2000000000000000000002-22-2
χ402-2-222-2-222-2-222-2-2200000022-2-222-2-2-22-2-2-22222-2-222-2-2200000000000000000000000000-2200000000000000000000-22-22
χ412-2-222-2-222-2-222-2-220000002-1-2-222-211-111-2-12-1-111-1-111-10000−i3i3−i3i3−i3i3i3−i3i3−i3−i3i300000000002-2000000000000−i3i3−i3i30000-11-11
χ422-2-222-2-222-2-222-2-220000002-1-2-222-211-111-2-12-1-111-1-111-10000−i3i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000-22000000000000i3−i3i3−i300001-11-1
χ432-2-222-2-222-2-222-2-220000002-1-2-222-211-111-2-12-1-111-1-111-10000i3−i3i3−i3i3−i3−i3i3−i3i3i3−i300000000002-2000000000000i3−i3i3−i30000-11-11
χ442-2-222-2-222-2-222-2-220000002-1-2-222-211-111-2-12-1-111-1-111-10000i3−i3i3−i3i3−i3−i3i3−i3i3i3−i30000000000-22000000000000−i3i3−i3i300001-11-1
χ452-2-2-2222-22-2-22-222-22i−2i2i2i−2i−2i22-2-22-22-2-2-22222-2-22-2-22-222-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ462-2-2-2222-22-2-22-222-22i−2i2i2i−2i−2i2-1-2-22-22111-1-12-1-21-111-11-1-112i−2i−2i2i−iii−i−iii−i−iii−i000000000000000000000000−i3i3i3−i300003−3−33
χ472-2-2-2222-22-2-22-222-22i−2i2i2i−2i−2i2-1-2-22-22111-1-12-1-21-111-11-1-112i−2i−2i2i−iii−i−iii−i−iii−i000000000000000000000000i3−i3−i3i30000−333−3
χ482-2-2-2222-22-2-22-222-22i−2i2i2i−2i−2i-1211-11-1-2-2-222-121-2-111-11-1-11−iii−i2i−2i−2i2i−iii−i−iii−i00000000000000000000−i3i3i3−i300003−3−330000
χ492-2-2-2222-22-2-22-222-22i−2i2i2i−2i−2i-1211-11-1-2-2-222-121-2-111-11-1-11−iii−i2i−2i−2i2i−iii−i−iii−i00000000000000000000i3−i3−i3i30000−333−30000
χ502-2-2-2222-22-2-22-222-2−2i2i−2i−2i2i2i22-2-22-22-2-2-22222-2-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ512-2-2-2222-22-2-22-222-2−2i2i−2i−2i2i2i2-1-2-22-22111-1-12-1-21-111-11-1-11−2i2i2i−2ii−i−iii−i−iii−i−ii000000000000000000000000−i3i3i3−i30000−333−3
χ522-2-2-2222-22-2-22-222-2−2i2i−2i−2i2i2i2-1-2-22-22111-1-12-1-21-111-11-1-11−2i2i2i−2ii−i−iii−i−iii−i−ii000000000000000000000000i3−i3−i3i300003−3−33
χ532-2-2-2222-22-2-22-222-2−2i2i−2i−2i2i2i-1211-11-1-2-2-222-121-2-111-11-1-11i−i−ii−2i2i2i−2ii−i−iii−i−ii00000000000000000000−i3i3i3−i30000−333−30000
χ542-2-2-2222-22-2-22-222-2−2i2i−2i−2i2i2i-1211-11-1-2-2-222-121-2-111-11-1-11i−i−ii−2i2i2i−2ii−i−iii−i−ii00000000000000000000i3−i3−i3i300003−3−330000
χ554444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ564444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ57444-44-4-4-44444-4-4-4-4000000-24-2-2-22244-4-4-4242-4-2-2-2-222220000000000000000000000000000000000000000000000000000
χ58444-44-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-22222-2221111-1-1-1-100002323−23−23−3−3−3−33333000000000000000000000000000000000000
χ59444-44-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-22222-2221111-1-1-1-10000−23−2323233333−3−3−3−3000000000000000000000000000000000000
χ6044-44-44-4-444-4-444-4-40000004-24-4-44-4-22-2-2242-42-2-222-2-2220000000000000000000000000000000000000000000000000000
χ6144-44-44-4-444-4-444-4-4000000-2-2-222-22-22-2-22-222211-1-111-1-12323−23−230000−3−333−3−333000000000000000000000000000000000000
χ6244-44-44-4-444-4-444-4-4000000-2-2-222-22-22-2-22-222211-1-111-1-1−23−232323000033−3−333−3−3000000000000000000000000000000000000
χ6344-4-4-4-44444-4-4-4-4440000004-24-4-4-44-2222-2-424-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ6444-4-4-4-44444-4-4-4-444000000-24-2222-24-4-4-442-4-24-2-22222-2-20000000000000000000000000000000000000000000000000000
χ6544-4-4-4-44444-4-4-4-444000000-2-2-2222-2-2222-222-2-211-1-1-1-1110000000033-3-3-3-333000000000000000000000000000000000000
χ6644-4-4-4-44444-4-4-4-444000000-2-2-2222-2-2222-222-2-211-1-1-1-11100000000-3-33333-3-3000000000000000000000000000000000000
χ674-444-4-44-44-44-44-44-40000004-2-44-4442-2-22-2-42-42-22-22-22-220000000000000000000000000000000000000000000000000000
χ684-444-4-44-44-44-44-44-4000000-242-22-2-2-444-442-42-4-22-22-22-220000000000000000000000000000000000000000000000000000
χ694-444-4-44-44-44-44-44-4000000-2-22-22-2-22-2-22-222221-11-11-11-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ704-444-4-44-44-44-44-44-4000000-2-22-22-2-22-2-22-222221-11-11-11-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ714-44-4-44-444-44-4-44-440000004-2-44-4-4-42-22-22424-2-22-222-22-20000000000000000000000000000000000000000000000000000
χ724-44-4-44-444-44-4-44-44000000-2-22-22222-22-22-22-2-21-11-1-11-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ734-44-4-44-444-44-4-44-44000000-2-22-22222-22-22-22-2-21-11-1-11-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ744-4-444-4-444-4-444-4-44000000-2422-2-22-4-44-4-424-24-222-2-222-20000000000000000000000000000000000000000000000000000
χ754-4-444-4-444-4-444-4-44000000-2-222-2-2222-2222-2-2-21-1-111-1-110000−2i32i3−2i32i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ764-4-444-4-444-4-444-4-44000000-2-222-2-2222-2222-2-2-21-1-111-1-1100002i3−2i32i3−2i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ774-4-4-4444-44-4-44-444-44i−4i4i4i−4i−4i-2-222-22-2222-2-2-2-2221-1-11-111-1−2i2i2i−2i−2i2i2i−2ii−i−iii−i−ii000000000000000000000000000000000000
χ784-4-4-4444-44-4-44-444-4−4i4i−4i−4i4i4i-2-222-22-2222-2-2-2-2221-1-11-111-12i−2i−2i2i2i−2i−2i2i−iii−i−iii−i000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000220000220000-1-1-1-1-1-1-1-10000000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-20000-2-20000111111110000000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000220000-2-20000-1-1-1-111110000000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-200002200001111-1-1-1-10000000000000000
χ8366-6-6-6-666-3-33333-3-300−3i33i3−3i33i300000000000000000000000000000000000000000000002-20000−i3i3−i3i3-1-1110000000000000000
χ8466-6-6-6-666-3-33333-3-300−3i33i3−3i33i30000000000000000000000000000000000000000000000-220000i3−i3i3−i311-1-10000000000000000
χ8566-6-6-6-666-3-33333-3-3003i3−3i33i3−3i300000000000000000000000000000000000000000000002-20000i3−i3i3−i3-1-1110000000000000000
χ8666-6-6-6-666-3-33333-3-3003i3−3i33i3−3i30000000000000000000000000000000000000000000000-220000−i3i3−i3i311-1-10000000000000000
χ876-666-6-66-6-33-33-33-330033−33−333300000000000000000000000000000000000000002-20000000000-1-1113−33−30000000000000000
χ886-666-6-66-6-33-33-33-330033−33−33330000000000000000000000000000000000000000-22000000000011-1-1−33−330000000000000000
χ896-666-6-66-6-33-33-33-3300−333333−3300000000000000000000000000000000000000002-20000000000-1-111−33−330000000000000000
χ906-666-6-66-6-33-33-33-3300−333333−330000000000000000000000000000000000000000-22000000000011-1-13−33−30000000000000000
χ916-6-6-6666-6-333-33-3-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000−i3i3i3−i33−3−330000000000000000
χ926-6-6-6666-6-333-33-3-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000i3−i3−i3i3−333−30000000000000000
χ936-6-6-6666-6-333-33-3-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000−i3i3i3−i3−333−30000000000000000
χ946-6-6-6666-6-333-33-3-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000i3−i3−i3i33−3−330000000000000000
χ95121212-1212-12-12-12-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-1212-1212-12-12-6-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-12-1212-1212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-121212-12-1212-666-6-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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