Finite Group Databasebeta

← Group #13140094

Character table — Group #13140094

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ922222222222222222222222-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ1022222222222222222222222-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ112222222222222222222222-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100220022000000000000-1-1-1-1-1-1-1-100000000
χ122222222222222222222222-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-200-2-20000000000001111111100000000
χ132222222222222222-2-2-2-2-2-22-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000022-2-20000000000000000-1-1-1-11111
χ142222222222222222-2-2-2-2-2-22-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000-2-22200000000000000001111-1-1-1-1
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-11111-2-2-2-211111111002200-2-2000000000000-1-1-1-1111100000000
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-11111-2-2-2-21111111100-2-200220000000000001111-1-1-1-100000000
χ17222-22-2-2-2222-2-2-22-200000022222-2222-2-2-2-2-2-2-22222-2-2-2-200000000000000002-2000000000022-2-200000000000000000000
χ18222-22-2-2-2222-2-2-22-200000022222-2222-2-2-2-2-2-2-22222-2-2-2-20000000000000000-220000000000-2-22200000000000000000000
χ1922-22-2-22-222-22-22-2-2000000222-2-2-22-2-2-2222-22-222-2-22-2-22000000000000000000002i−2i00000000002i2i−2i−2i0000000000000000
χ2022-22-2-22-222-22-22-2-2000000222-2-2-22-2-2-2222-22-222-2-22-2-2200000000000000000000−2i2i0000000000−2i−2i2i2i0000000000000000
χ2122-2-2-22-2222-2-22-2-222i−2i2i2i−2i−2i222-2-222-2-22-2-2-22-2222-2-2-222-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ2222-2-2-22-2222-2-22-2-222i−2i2i2i−2i−2i2-12-2-22-111-1-21-221-1-1-1111-1-112i2i−2i−2i−i−iii−i−i−i−iiiii0000000000000000000000000000−i3−i3i3i333−3−3
χ2322-2-2-22-2222-2-22-2-222i−2i2i2i−2i−2i2-12-2-22-111-1-21-221-1-1-1111-1-112i2i−2i−2i−i−iii−i−i−i−iiiii0000000000000000000000000000i3i3−i3−i3−3−333
χ2422-2-2-22-2222-2-22-2-222i−2i2i2i−2i−2i-12-111-12-2-221-21-1-22-1-1111-1-11−i−iii2i2i−2i−2i−i−i−i−iiiii00000000000000000000−i3−i3i3i333−3−300000000
χ2522-2-2-22-2222-2-22-2-222i−2i2i2i−2i−2i-12-111-12-2-221-21-1-22-1-1111-1-11−i−iii2i2i−2i−2i−i−i−i−iiiii00000000000000000000i3i3−i3−i3−3−33300000000
χ2622-2-2-22-2222-2-22-2-22−2i2i−2i−2i2i2i222-2-222-2-22-2-2-22-2222-2-2-222-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ2722-2-2-22-2222-2-22-2-22−2i2i−2i−2i2i2i2-12-2-22-111-1-21-221-1-1-1111-1-11−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000000000000000000000−i3−i3i3i3−3−333
χ2822-2-2-22-2222-2-22-2-22−2i2i−2i−2i2i2i2-12-2-22-111-1-21-221-1-1-1111-1-11−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000000000000000000000i3i3−i3−i333−3−3
χ2922-2-2-22-2222-2-22-2-22−2i2i−2i−2i2i2i-12-111-12-2-221-21-1-22-1-1111-1-11ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000000000000000−i3−i3i3i3−3−33300000000
χ3022-2-2-22-2222-2-22-2-22−2i2i−2i−2i2i2i-12-111-12-2-221-21-1-22-1-1111-1-11ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000000000000000i3i3−i3−i333−3−300000000
χ312-222-2-2-222-22-2-22-2200000022-22-22-22-2-222-2-2-222-22-2-22-220000000000000000002i−2i00000000000000002i−2i2i−2i000000000000
χ322-222-2-2-222-22-2-22-2200000022-22-22-22-2-222-2-2-222-22-2-22-22000000000000000000−2i2i0000000000000000−2i2i−2i2i000000000000
χ332-222-2-2-222-22-2-22-22000000-121-11-1-22-2-2-1211-22-11-111-11-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3002i−2i0000000000000000−ii−ii3−33−300000000
χ342-222-2-2-222-22-2-22-22000000-121-11-1-22-2-2-1211-22-11-111-11-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i300−2i2i0000000000000000i−ii−i−33−3300000000
χ352-222-2-2-222-22-2-22-22000000-121-11-1-22-2-2-1211-22-11-111-11-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3002i−2i0000000000000000−ii−ii−33−3300000000
χ362-222-2-2-222-22-2-22-22000000-121-11-1-22-2-2-1211-22-11-111-11-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i300−2i2i0000000000000000i−ii−i3−33−300000000
χ372-22-2-222-22-2222-2-2-200000022-22-2-2-22-22-2-2222-22-22-22-22-20000000000000000000000002i−2i0000000000000000002i−2i2i−2i0000
χ382-22-2-222-22-2222-2-2-200000022-22-2-2-22-22-2-2222-22-22-22-22-2000000000000000000000000−2i2i000000000000000000−2i2i−2i2i0000
χ392-22-2-222-22-2222-2-2-20000002-1-22-2-21-11-1-2122-11-11-11-11-1100003−33−33−33−33−33−3000000002i−2i000000000000000000−ii−ii−i3i3−i3i3
χ402-22-2-222-22-2222-2-2-20000002-1-22-2-21-11-1-2122-11-11-11-11-1100003−33−33−33−33−33−300000000−2i2i000000000000000000i−ii−ii3−i3i3−i3
χ412-22-2-222-22-2222-2-2-20000002-1-22-2-21-11-1-2122-11-11-11-11-110000−33−33−33−33−33−33000000002i−2i000000000000000000−ii−iii3−i3i3−i3
χ422-22-2-222-22-2222-2-2-20000002-1-22-2-21-11-1-2122-11-11-11-11-110000−33−33−33−33−33−3300000000−2i2i000000000000000000i−ii−i−i3i3−i3i3
χ432-2-2222-2-22-2-2-2222-200000022-2-22-2-2-22222-22-2-22-2-22-2-222000000000000000000000000002i−2i000000000000000000002i−2i−2i2i
χ442-2-2222-2-22-2-2-2222-200000022-2-22-2-2-22222-22-2-22-2-22-2-22200000000000000000000000000−2i2i00000000000000000000−2i2i2i−2i
χ452-2-2222-2-22-2-2-2222-20000002-1-2-22-211-1-12-1-2211-111-111-1-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i300000000002i−2i0000000000000000−333−3−iii−i
χ462-2-2222-2-22-2-2-2222-20000002-1-2-22-211-1-12-1-2211-111-111-1-10000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i30000000000−2i2i00000000000000003−3−33i−i−ii
χ472-2-2222-2-22-2-2-2222-20000002-1-2-22-211-1-12-1-2211-111-111-1-10000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i300000000002i−2i00000000000000003−3−33−iii−i
χ482-2-2222-2-22-2-2-2222-20000002-1-2-22-211-1-12-1-2211-111-111-1-10000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i30000000000−2i2i0000000000000000−333−3i−i−ii
χ492-2-2-22-2222-2-22-2-22200000022-2-222-2-22-2-2-22-2222-2-2222-2-200000000000000000000002-200000000000000002-2-2200000000
χ502-2-2-22-2222-2-22-2-22200000022-2-222-2-22-2-2-22-2222-2-2222-2-20000000000000000000000-220000000000000000-222-200000000
χ512-2-2-22-2222-2-22-2-222000000-1211-1-1-2-22-21-2-1122-111-1-1-1113−3−33000033−3−3−3−3330000002-2000000000000−333−3-111-100000000
χ522-2-2-22-2222-2-22-2-222000000-1211-1-1-2-22-21-2-1122-111-1-1-1113−3−33000033−3−3−3−333000000-220000000000003−3−331-1-1100000000
χ532-2-2-22-2222-2-22-2-222000000-1211-1-1-2-22-21-2-1122-111-1-1-111−333−30000−3−33333−3−30000002-20000000000003−3−33-111-100000000
χ542-2-2-22-2222-2-22-2-222000000-1211-1-1-2-22-21-2-1122-111-1-1-111−333−30000−3−33333−3−3000000-22000000000000−333−31-1-1100000000
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
χ57444-44-4-4-4444-4-4-44-40000004-2444-4-2-2-22-42-4-422-2-2-2-222220000000000000000000000000000000000000000000000000000
χ58444-44-4-4-4444-4-4-44-4000000-24-2-2-22444-42-422-4-4-2-2-2-222220000000000000000000000000000000000000000000000000000
χ59444-44-4-4-4444-4-4-44-4000000-2-2-2-2-22-2-2-222222221111-1-1-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000
χ60444-44-4-4-4444-4-4-44-4000000-2-2-2-2-22-2-2-222222221111-1-1-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000
χ6144-44-4-44-444-44-44-4-40000004-24-4-4-4-22224-24-4-22-2-222-222-20000000000000000000000000000000000000000000000000000
χ6244-44-4-44-444-44-44-4-4000000-24-22224-4-4-4-24-224-4-2-222-222-20000000000000000000000000000000000000000000000000000
χ6344-44-4-44-444-44-44-4-4000000-2-2-2222-2222-2-2-22-2211-1-11-1-11000000003-3-33-333-3000000000000000000000000000000000000
χ6444-44-4-44-444-44-44-4-4000000-2-2-2222-2222-2-2-22-2211-1-11-1-1100000000-333-33-3-33000000000000000000000000000000000000
χ6544-4-4-44-4444-4-44-4-444i−4i4i4i−4i−4i-2-2-222-2-222-2222-22-211-1-1-111-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i000000000000000000000000000000000000
χ6644-4-4-44-4444-4-44-4-44−4i4i−4i−4i4i4i-2-2-222-2-222-2222-22-211-1-1-111-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000
χ674-444-4-4-444-44-4-44-440000004-2-44-442-2224-2-4-42-2-22-222-22-20000000000000000000000000000000000000000000000000000
χ684-444-4-4-444-44-4-44-44000000-2-22-22-22-222-2-2222-21-11-1-11-11−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ694-444-4-4-444-44-4-44-44000000-2-22-22-22-222-2-2222-21-11-1-11-112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ704-44-4-444-44-4444-4-4-4000000-242-222-44-442-4-2-24-4-22-22-22-220000000000000000000000000000000000000000000000000000
χ714-44-4-444-44-4444-4-4-4000000-2-22-2222-22-222-2-2-221-11-11-11-1000023−2323−23−33−33−33−33000000000000000000000000000000000000
χ724-44-4-444-44-4444-4-4-4000000-2-22-2222-22-222-2-2-221-11-11-11-10000−2323−23233−33−33−33−3000000000000000000000000000000000000
χ734-4-4444-4-44-4-4-4444-4000000-2422-22-4-444-242-2-4-4-222-222-2-20000000000000000000000000000000000000000000000000000
χ744-4-4444-4-44-4-4-4444-4000000-2-222-2222-2-2-2-22-2221-1-11-1-1110000−2i32i32i3−2i3i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000
χ754-4-4444-4-44-4-4-4444-4000000-2-222-2222-2-2-2-22-2221-1-11-1-11100002i3−2i3−2i32i3−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000
χ764-4-4-44-4444-4-44-4-4440000004-2-4-44422-22-424-4-2-2-222-2-2-2220000000000000000000000000000000000000000000000000000
χ774-4-4-44-4444-4-44-4-444000000-2-222-2-222-2222-22-2-21-1-1111-1-123−23−23230000−3−33333−3−3000000000000000000000000000000000000
χ784-4-4-44-4444-4-44-4-444000000-2-222-2-222-2222-22-2-21-1-1111-1-1−232323−23000033−3−3−3−333000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000220022000000-1-1-1-1-1-1-1-10000000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-200-2-2000000111111110000000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000002200-2-2000000-1-1-1-111110000000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-200220000001111-1-1-1-10000000000000000
χ83666-66-6-6-6-3-3-3333-330033−3333−3300000000000000000000000000000000000000002-20000000000-1-1113−33−30000000000000000
χ84666-66-6-6-6-3-3-3333-330033−3333−330000000000000000000000000000000000000000-22000000000011-1-1−33−330000000000000000
χ85666-66-6-6-6-3-3-3333-3300−3333−333300000000000000000000000000000000000000002-20000000000-1-111−33−330000000000000000
χ86666-66-6-6-6-3-3-3333-3300−3333−33330000000000000000000000000000000000000000-22000000000011-1-13−33−30000000000000000
χ8766-66-6-66-6-3-33-33-33300−3i33i33i3−3i3000000000000000000000000000000000000000000002i−2i0000003−33−3−i−iii0000000000000000
χ8866-66-6-66-6-3-33-33-33300−3i33i33i3−3i300000000000000000000000000000000000000000000−2i2i000000−33−33ii−i−i0000000000000000
χ8966-66-6-66-6-3-33-33-333003i3−3i3−3i33i3000000000000000000000000000000000000000000002i−2i000000−33−33−i−iii0000000000000000
χ9066-66-6-66-6-3-33-33-333003i3−3i3−3i33i300000000000000000000000000000000000000000000−2i2i0000003−33−3ii−i−i0000000000000000
χ9166-6-6-66-66-3-333-333-36i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000003−3−33i3−i3−i3i30000000000000000
χ9266-6-6-66-66-3-333-333-36i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000−333−3−i3i3i3−i30000000000000000
χ9366-6-6-66-66-3-333-333-3−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000003−3−33−i3i3i3−i30000000000000000
χ9466-6-6-66-66-3-333-333-3−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000−333−3i3−i3−i3i30000000000000000
χ9512-121212-12-12-1212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-12-121212-12-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-12121212-12-12-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-12-1212-121212-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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