Finite Group Databasebeta

← Group #13141168

Character table — Group #13141168

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666226666336666666666666636666666666666666666666622444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ922222222222222222222222-122222-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000002200-1-1-1-100000000-1-1-1-100000000
χ1022222222222222222222222-122222-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000-2-200111100000000111100000000
χ112222222222222222222222-12-1-1-1-1-1222222-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-1-1222222-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2000000000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-122-1-1-2-2-2-21111-1-1-1-1-1-1-11111111122000000-2-200-1-1-1-100000000111100000000
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-122-1-1-2-2-2-21111-1-1-1-1-1-1-111111111-2-20000002200111100000000-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-1-12-11111-2-2-2-2-1-1-1-1-1-1-1111111110022-2-20000000000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-1-12-11111-2-2-2-2-1-1-1-1-1-1-11111111100-2-22200000000000000000000001111-1-1-1-1
χ17222-22-2-2-22222-2-2-2-20000002222-2-2-2222-2-2-22-2-2200000000222-2-2-2-20000000000000000002i−2i000000002i2i−2i−2i000000000000
χ18222-22-2-2-22222-2-2-2-20000002222-2-2-2222-2-2-22-2-2200000000222-2-2-2-2000000000000000000−2i2i00000000−2i−2i2i2i000000000000
χ1922-22-22-2-222-2-222-2-2000000222-22-2-22-2-222-2-22-22000000002-2-222-2-2000000000000002i−2i000000002i2i−2i−2i0000000000000000
χ2022-22-22-2-222-2-222-2-2000000222-22-2-22-2-222-2-22-22000000002-2-222-2-200000000000000−2i2i00000000−2i−2i2i2i0000000000000000
χ2122-2-2-2-22222-2-2-2-2222-222-2-2222-2-2222-2-2-2-22-2-22222-2-222-2-22-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000
χ2222-2-2-2-22222-2-2-2-2222-222-2-22-12-2-222-11111-1-2-2-1-122-2-2-1-111-11111-1-1-1-1-1-11111000000000000−i3−i3i3i300000000−i3−i3i3i300000000
χ2322-2-2-2-22222-2-2-2-2222-222-2-22-12-2-222-11111-1-2-2-1-122-2-2-1-111-11111-1-1-1-1-1-11111000000000000i3i3−i3−i300000000i3i3−i3−i300000000
χ2422-2-2-2-22222-2-2-2-2222-222-2-2-12-111-1-12-2-2-2-22112-1-1-11122-2-2-11111-1-1-1-1-1-11111000000000000000000000000000033−3−333−3−3
χ2522-2-2-2-22222-2-2-2-2222-222-2-2-12-111-1-12-2-2-2-22112-1-1-11122-2-2-11111-1-1-1-1-1-111110000000000000000000000000000−3−333−3−333
χ2622-2-2-2-22222-2-2-2-222-22-2-222222-2-2222-2-2-2-22-2-222-2-222-2-2222-2-2-2-222-2-2-2-22222000000000000000000000000000000000000
χ2722-2-2-2-22222-2-2-2-222-22-2-2222-12-2-222-11111-1-2-2-1-1-2-22211-1-1-11111-1-11111-1-1-1-1000000000000−i3−i3i3i300000000i3i3−i3−i300000000
χ2822-2-2-2-22222-2-2-2-222-22-2-2222-12-2-222-11111-1-2-2-1-1-2-22211-1-1-11111-1-11111-1-1-1-1000000000000i3i3−i3−i300000000−i3−i3i3i300000000
χ2922-2-2-2-22222-2-2-2-222-22-2-222-12-111-1-12-2-2-2-22112-111-1-1-2-222-11111-1-11111-1-1-1-1000000000000000000000000000033−3−3−3−333
χ3022-2-2-2-22222-2-2-2-222-22-2-222-12-111-1-12-2-2-2-22112-111-1-1-2-222-11111-1-11111-1-1-1-10000000000000000000000000000−3−33333−3−3
χ312-222-2-22-22-22-22-22-200000022-2222-2-22-22-22-2-2-2200000000-22-22-22-20000000000002i−2i000000000000000000000000002i−2i2i−2i
χ322-222-2-22-22-22-22-22-200000022-2222-2-22-22-22-2-2-2200000000-22-22-22-2000000000000−2i2i00000000000000000000000000−2i2i−2i2i
χ332-222-2-22-22-22-22-22-2000000-121-1-1-11-22-22-2211-2-1−i3i3−i3i300001-11-11-11−i3−i3i3i3−i3−i3i3i300002i−2i00000000000000000000003−33−3−ii−ii
χ342-222-2-22-22-22-22-22-2000000-121-1-1-11-22-22-2211-2-1−i3i3−i3i300001-11-11-11−i3−i3i3i3−i3−i3i3i30000−2i2i0000000000000000000000−33−33i−ii−i
χ352-222-2-22-22-22-22-22-2000000-121-1-1-11-22-22-2211-2-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i300002i−2i0000000000000000000000−33−33−ii−ii
χ362-222-2-22-22-22-22-22-2000000-121-1-1-11-22-22-2211-2-1i3−i3i3−i300001-11-11-11i3i3−i3−i3i3i3−i3−i30000−2i2i00000000000000000000003−33−3i−ii−i
χ372-22-2-22-222-22-2-22-2200000022-22-2-22-22-2-22-2-222200000000-22-2-22-22000000002-200000000002-22-200000000000000000000
χ382-22-2-22-222-22-2-22-2200000022-22-2-22-22-2-22-2-222200000000-22-2-22-2200000000-220000000000-22-2200000000000000000000
χ392-22-2-22-222-22-2-22-220000002-1-22-2-221-111-11-22-1-10000−i3i3−i3i31-111-11-1−i3i3−i3i3−i3i3−i3i32-20000000000-11-1100000000−i3i3−i3i300000000
χ402-22-2-22-222-22-2-22-220000002-1-22-2-221-111-11-22-1-10000−i3i3−i3i31-111-11-1−i3i3−i3i3−i3i3−i3i3-2200000000001-11-100000000i3−i3i3−i300000000
χ412-22-2-22-222-22-2-22-220000002-1-22-2-221-111-11-22-1-10000i3−i3i3−i31-111-11-1i3−i3i3−i3i3−i3i3−i32-20000000000-11-1100000000i3−i3i3−i300000000
χ422-22-2-22-222-22-2-22-220000002-1-22-2-221-111-11-22-1-10000i3−i3i3−i31-111-11-1i3−i3i3−i3i3−i3i3−i3-2200000000001-11-100000000−i3i3−i3i300000000
χ432-2-222-2-222-2-222-2-2200000022-2-22-22-2-222-2-22-22200000000-2-222-2-2200000000000000002-2000000000000002-2-2200000000
χ442-2-222-2-222-2-222-2-2200000022-2-22-22-2-222-2-22-22200000000-2-222-2-220000000000000000-2200000000000000-222-200000000
χ452-2-222-2-222-2-222-2-220000002-1-2-22-2211-1-1112-2-1-10000−i3i3i3−i311-1-111-1−i3i3−i3i3i3−i3i3−i3000000002-200−i3i3i3−i300000000-111-100000000
χ462-2-222-2-222-2-222-2-220000002-1-2-22-2211-1-1112-2-1-10000−i3i3i3−i311-1-111-1−i3i3−i3i3i3−i3i3−i300000000-2200i3−i3−i3i3000000001-1-1100000000
χ472-2-222-2-222-2-222-2-220000002-1-2-22-2211-1-1112-2-1-10000i3−i3−i3i311-1-111-1i3−i3i3−i3−i3i3−i3i3000000002-200i3−i3−i3i300000000-111-100000000
χ482-2-222-2-222-2-222-2-220000002-1-2-22-2211-1-1112-2-1-10000i3−i3−i3i311-1-111-1i3−i3i3−i3−i3i3−i3i300000000-2200−i3i3i3−i3000000001-1-1100000000
χ492-2-2-2222-22-2-22-222-200000022-2-2-22-2-2-22-22222-2200000000-2-22-222-200000000002-20000000000000000000000002-2-220000
χ502-2-2-2222-22-2-22-222-200000022-2-2-22-2-2-22-22222-2200000000-2-22-222-20000000000-22000000000000000000000000-222-20000
χ512-2-2-2222-22-2-22-222-2000000-12111-11-2-22-222-1-1-2-1−i3i3i3−i3000011-11-1-11−i3−i3i3i3i3i3−i3−i3002-2000000000000000000000000-111-1−i3i3i3−i3
χ522-2-2-2222-22-2-22-222-2000000-12111-11-2-22-222-1-1-2-1−i3i3i3−i3000011-11-1-11−i3−i3i3i3i3i3−i3−i300-220000000000000000000000001-1-11i3−i3−i3i3
χ532-2-2-2222-22-2-22-222-2000000-12111-11-2-22-222-1-1-2-1i3−i3−i3i3000011-11-1-11i3i3−i3−i3−i3−i3i3i3002-2000000000000000000000000-111-1i3−i3−i3i3
χ542-2-2-2222-22-2-22-222-2000000-12111-11-2-22-222-1-1-2-1i3−i3−i3i3000011-11-1-11i3i3−i3−i3−i3−i3i3i300-220000000000000000000000001-1-11−i3i3i3−i3
χ554444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2111111111111111000000000000000000000000000000000000
χ564444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21222222221111111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ57444-44-4-4-44444-4-4-4-40000004-244-4-4-4-2-2-22224-42-200000000-2-2-2222200000000000000000000000000000000000000000000
χ58444-44-4-4-44444-4-4-4-4000000-24-2-2222444-4-4-4-22-4-200000000-2-2-2222200000000000000000000000000000000000000000000
χ59444-44-4-4-44444-4-4-4-4000000-2-2-2-2222-2-2-2222-222100000000111-1-1-1-13-3-333-3-33000000000000000000000000000000000000
χ60444-44-4-4-44444-4-4-4-4000000-2-2-2-2222-2-2-2222-222100000000111-1-1-1-1-333-3-333-3000000000000000000000000000000000000
χ6144-44-44-4-444-4-444-4-40000004-24-44-4-4-222-2-22-442-200000000-222-2-22200000000000000000000000000000000000000000000
χ6244-44-44-4-444-4-444-4-4000000-24-22-2224-4-444-42-2-4-200000000-222-2-22200000000000000000000000000000000000000000000
χ6344-44-44-4-444-4-444-4-4000000-2-2-22-222-222-2-222-221000000001-1-111-1-13-3-33-333-3000000000000000000000000000000000000
χ6444-44-44-4-444-4-444-4-4000000-2-2-22-222-222-2-222-221000000001-1-111-1-1-333-33-3-33000000000000000000000000000000000000
χ6544-4-4-4-44444-4-4-4-4444-444-4-4-2-2-222-2-2-22222-222-21-2-222-2-2221-1-1-1-1111111-1-1-1-1000000000000000000000000000000000000
χ6644-4-4-4-44444-4-4-4-444-44-4-444-2-2-222-2-2-22222-222-2122-2-222-2-21-1-1-1-111-1-1-1-11111000000000000000000000000000000000000
χ674-444-4-44-44-44-44-44-40000004-2-4444-42-22-22-2-4-42-2000000002-22-22-2200000000000000000000000000000000000000000000
χ684-444-4-44-44-44-44-44-4000000-2-22-2-2-222-22-22-22221−2i32i3−2i32i30000-11-11-11-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ694-444-4-44-44-44-44-44-4000000-2-22-2-2-222-22-22-222212i3−2i32i3−2i30000-11-11-11-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ704-44-4-44-444-44-4-44-44000000-242-222-2-44-4-44-42-24-2000000002-222-22-200000000000000000000000000000000000000000000
χ714-44-4-44-444-44-4-44-44000000-2-22-222-22-222-222-2-210000−2i32i3−2i32i3-11-1-11-11i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ724-44-4-44-444-44-4-44-44000000-2-22-222-22-222-222-2-2100002i3−2i32i3−2i3-11-1-11-11−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ734-4-444-4-444-4-444-4-44000000-2422-22-2-4-444-4-4-224-20000000022-2-222-200000000000000000000000000000000000000000000
χ744-4-444-4-444-4-444-4-44000000-2-222-22-222-2-222-22-210000−2i32i32i3−2i3-1-111-1-11i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000
χ754-4-444-4-444-4-444-4-44000000-2-222-22-222-2-222-22-2100002i3−2i3−2i32i3-1-111-1-11−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000
χ764-4-4-4444-44-4-44-444-40000004-2-4-4-44-422-22-2-2442-20000000022-22-2-2200000000000000000000000000000000000000000000
χ774-4-4-4444-44-4-44-444-4000000-2-2222-2222-22-2-2-2-221−2i32i32i3−2i30000-1-11-111-1i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000
χ784-4-4-4444-44-4-44-444-4000000-2-2222-2222-22-2-2-2-2212i3−2i3−2i32i30000-1-11-111-1−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000002200220000-1-1-1-1-1-1-1-1000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000000000-2-200-2-2000011111111000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000002200-2-20000-1-1-1-11111000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000000000-2-2002200001111-1-1-1-1000000000000
χ83666-66-6-6-6-3-3-3-3333300−3i33i3−3i33i3000000000000000000000000000000000000000000000000002i−2i00003−33−3−i−iii000000000000
χ84666-66-6-6-6-3-3-3-3333300−3i33i3−3i33i300000000000000000000000000000000000000000000000000−2i2i0000−33−33ii−i−i000000000000
χ85666-66-6-6-6-3-3-3-33333003i3−3i33i3−3i3000000000000000000000000000000000000000000000000002i−2i0000−33−33−i−iii000000000000
χ86666-66-6-6-6-3-3-3-33333003i3−3i33i3−3i300000000000000000000000000000000000000000000000000−2i2i00003−33−3ii−i−i000000000000
χ8766-66-66-6-6-3-333-3-33300−3i33i33i3−3i300000000000000000000000000000000000000000000002i−2i00000000−i−iii3−33−3000000000000
χ8866-66-66-6-6-3-333-3-33300−3i33i33i3−3i30000000000000000000000000000000000000000000000−2i2i00000000ii−i−i−33−33000000000000
χ8966-66-66-6-6-3-333-3-333003i3−3i3−3i33i300000000000000000000000000000000000000000000002i−2i00000000−i−iii−33−33000000000000
χ9066-66-66-6-6-3-333-3-333003i3−3i3−3i33i30000000000000000000000000000000000000000000000−2i2i00000000ii−i−i3−33−3000000000000
χ9166-6-6-6-666-3-33333-3-36-6-3-33300000000000000000000000000000000000000000000000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ9266-6-6-6-666-3-33333-3-36-6-3-33300000000000000000000000000000000000000000000000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ9366-6-6-6-666-3-33333-3-3-6633-3-300000000000000000000000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i3000000000000
χ9466-6-6-6-666-3-33333-3-3-6633-3-300000000000000000000000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i3000000000000
χ9512-121212-12-1212-12-66-66-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-12-1212-1212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-121212-12-1212-666-6-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-12-12121212-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000

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