Finite Group Databasebeta

← Group #13140143

Character table — Group #13140143

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111
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
χ922222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1220022000000-1-1-1-100000000-1-1-1-100000000
χ1022222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2000000111100000000111100000000
χ112222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111112200-2-2000000-1-1-1-100000000111100000000
χ142222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-20022000000111100000000-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111110000000022-2-20000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-22200000000000000001111-1-1-1-1
χ172222-2-2-2-22222-2-2-2-200000022222-2222-2-2-2-2-2-2-22222-2-2-2-200000000000000002-2000000000022-2-200000000000000000000
χ182222-2-2-2-22222-2-2-2-200000022222-2222-2-2-2-2-2-2-22222-2-2-2-20000000000000000-220000000000-2-22200000000000000000000
χ192222-2-2-2-22222-2-2-2-20000002-1222-2-1-1-111-21-2-21-1-1-1-11111000033−3−33333−3−3−3−32-20000000000-1-1110000000033−3−300000000
χ202222-2-2-2-22222-2-2-2-20000002-1222-2-1-1-111-21-2-21-1-1-1-11111000033−3−33333−3−3−3−3-22000000000011-1-100000000−3−33300000000
χ212222-2-2-2-22222-2-2-2-20000002-1222-2-1-1-111-21-2-21-1-1-1-111110000−3−333−3−3−3−333332-20000000000-1-11100000000−3−33300000000
χ222222-2-2-2-22222-2-2-2-20000002-1222-2-1-1-111-21-2-21-1-1-1-111110000−3−333−3−3−3−33333-22000000000011-1-10000000033−3−300000000
χ2322-2-222-2-222-2-22-2-22000000222-2-222-2-22-222-2-2-222-2-22-2-22000000000000000000000000002i−2i000000000000000000002i2i−2i−2i
χ2422-2-222-2-222-2-22-2-22000000222-2-222-2-22-222-2-2-222-2-22-2-2200000000000000000000000000−2i2i00000000000000000000−2i−2i2i2i
χ2522-2-222-2-222-2-22-2-22000000-12-111-12-2-22-2-1211-2-1-111-111-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i300000000002i−2i000000000000000033−3−3−i−iii
χ2622-2-222-2-222-2-22-2-22000000-12-111-12-2-22-2-1211-2-1-111-111-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i30000000000−2i2i0000000000000000−3−333ii−i−i
χ2722-2-222-2-222-2-22-2-22000000-12-111-12-2-22-2-1211-2-1-111-111-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i300000000002i−2i0000000000000000−3−333−i−iii
χ2822-2-222-2-222-2-22-2-22000000-12-111-12-2-22-2-1211-2-1-111-111-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i30000000000−2i2i000000000000000033−3−3ii−i−i
χ2922-2-2-2-22222-2-2-222-2000000222-2-2-22-2-2-22-2-222222-2-2-222-200000000000000000000002-20000000022-2-20000000000000000
χ3022-2-2-2-22222-2-2-222-2000000222-2-2-22-2-2-22-2-222222-2-2-222-20000000000000000000000-2200000000-2-2220000000000000000
χ312-22-22-22-22-22-222-2-200000022-22-22-22-22-2-2-22-222-22-222-2-20000000000000000000000002i−2i0000000000000000002i−2i2i−2i0000
χ322-22-22-22-22-22-222-2-200000022-22-22-22-22-2-2-22-222-22-222-2-2000000000000000000000000−2i2i000000000000000000−2i2i−2i2i0000
χ332-22-22-22-22-22-222-2-2000000-121-11-1-22-22-21-2-112-11-11-1-1113−33−300003−33−33−33−3000000002i−2i000000000000000000−ii−ii−i3i3−i3i3
χ342-22-22-22-22-22-222-2-2000000-121-11-1-22-22-21-2-112-11-11-1-1113−33−300003−33−33−33−300000000−2i2i000000000000000000i−ii−ii3−i3i3−i3
χ352-22-22-22-22-22-222-2-2000000-121-11-1-22-22-21-2-112-11-11-1-111−33−330000−33−33−33−33000000002i−2i000000000000000000−ii−iii3−i3i3−i3
χ362-22-22-22-22-22-222-2-2000000-121-11-1-22-22-21-2-112-11-11-1-111−33−330000−33−33−33−3300000000−2i2i000000000000000000i−ii−i−i3i3−i3i3
χ372-22-2-22-222-22-2-2-22200000022-22-2-2-22-2-2222-22-22-22-2-2-2220000000000000000002-2000000000000000022-2-2000000000000
χ382-22-2-22-222-22-2-2-22200000022-22-2-2-22-2-2222-22-22-22-2-2-222000000000000000000-220000000000000000-2-222000000000000
χ392-2-222-2-222-2-222-22-22i−2i2i2i−2i−2i22-2-222-2-2222-2-2-22-22-2-222-22-22i−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ402-2-222-2-222-2-222-22-22i−2i2i2i−2i−2i2-1-2-22211-1-1-1-21-221-111-1-11-112i−2i−2i2i−ii−ii−iii−i−iii−i000000000000−i3i3−i3i3000000003−33−300000000
χ412-2-222-2-222-2-222-22-22i−2i2i2i−2i−2i2-1-2-22211-1-1-1-21-221-111-1-11-112i−2i−2i2i−ii−ii−iii−i−iii−i000000000000i3−i3i3−i300000000−33−3300000000
χ422-2-222-2-222-2-222-22-22i−2i2i2i−2i−2i-1211-1-1-2-22221-21-1-2-111-1-11-11−iii−i2i−2i2i−2i−iii−i−iii−i0000000000000000000000000000−i3i3i3−i3−333−3
χ432-2-222-2-222-2-222-22-22i−2i2i2i−2i−2i-1211-1-1-2-22221-21-1-2-111-1-11-11−iii−i2i−2i2i−2i−iii−i−iii−i0000000000000000000000000000i3−i3−i3i33−3−33
χ442-2-222-2-222-2-222-22-2−2i2i−2i−2i2i2i22-2-222-2-2222-2-2-22-22-2-222-22-2−2i2i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ452-2-222-2-222-2-222-22-2−2i2i−2i−2i2i2i2-1-2-22211-1-1-1-21-221-111-1-11-11−2i2i2i−2ii−ii−ii−i−iii−i−ii000000000000−i3i3−i3i300000000−33−3300000000
χ462-2-222-2-222-2-222-22-2−2i2i−2i−2i2i2i2-1-2-22211-1-1-1-21-221-111-1-11-11−2i2i2i−2ii−ii−ii−i−iii−i−ii000000000000i3−i3i3−i3000000003−33−300000000
χ472-2-222-2-222-2-222-22-2−2i2i−2i−2i2i2i-1211-1-1-2-22221-21-1-2-111-1-11-11i−i−ii−2i2i−2i2ii−i−iii−i−ii0000000000000000000000000000−i3i3i3−i33−3−33
χ482-2-222-2-222-2-222-22-2−2i2i−2i−2i2i2i-1211-1-1-2-22221-21-1-2-111-1-11-11i−i−ii−2i2i−2i2ii−i−iii−i−ii0000000000000000000000000000i3−i3−i3i3−333−3
χ492-2-22-222-22-2-22-22-2200000022-2-22-2-2-22-2-2222-222-2-22-22-22000000000000000000002-20000000000000000002-2-2200000000
χ502-2-22-222-22-2-22-22-2200000022-2-22-2-2-22-2-2222-222-2-22-22-2200000000000000000000-22000000000000000000-222-200000000
χ512-2-22-222-22-2-22-22-220000002-1-2-22-211-1112-12-2-1-111-11-11-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300002-2000000−i3i3i3−i300000000-111-100000000
χ522-2-22-222-22-2-22-22-220000002-1-2-22-211-1112-12-2-1-111-11-11-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000-22000000i3−i3−i3i3000000001-1-1100000000
χ532-2-22-222-22-2-22-22-220000002-1-2-22-211-1112-12-2-1-111-11-11-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300002-2000000i3−i3−i3i300000000-111-100000000
χ542-2-22-222-22-2-22-22-220000002-1-2-22-211-1112-12-2-1-111-11-11-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000-22000000−i3i3i3−i3000000001-1-1100000000
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
χ574444-4-4-4-44444-4-4-4-4000000-24-2-2-22444-4-42-422-4-2-2-2-222220000000000000000000000000000000000000000000000000000
χ584444-4-4-4-44444-4-4-4-4000000-2-2-2-2-22-2-2-222222221111-1-1-1-100002323−23−23−3−3−3−33333000000000000000000000000000000000000
χ594444-4-4-4-44444-4-4-4-4000000-2-2-2-2-22-2-2-222222221111-1-1-1-10000−23−2323233333−3−3−3−3000000000000000000000000000000000000
χ6044-4-444-4-444-4-44-4-440000004-24-4-44-222-224-2-4-42-2-222-222-20000000000000000000000000000000000000000000000000000
χ6144-4-444-4-444-4-44-4-44000000-2-2-222-2-222-22-2-222211-1-11-1-11−2i3−2i32i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ6244-4-444-4-444-4-44-4-44000000-2-2-222-2-222-22-2-222211-1-11-1-112i32i3−2i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ6344-4-4-4-44444-4-4-444-40000004-24-4-4-4-2222-2-4244-2-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6444-4-4-4-44444-4-4-444-4000000-24-22224-4-4-442-4-2-24-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6544-4-4-4-44444-4-4-444-4000000-2-2-2222-2222-222-2-2-211-1-1-111-1000000003i3i−3i−3i−3i−3i3i3i000000000000000000000000000000000000
χ6644-4-4-4-44444-4-4-444-4000000-2-2-2222-2222-222-2-2-211-1-1-111-100000000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000000000000
χ674-44-44-44-44-44-444-4-40000004-2-44-442-22-22-424-4-2-22-22-2-2220000000000000000000000000000000000000000000000000000
χ684-44-44-44-44-44-444-4-4000000-2-22-22-22-22-2222-22-21-11-111-1-123−2323−230000−33−33−33−33000000000000000000000000000000000000
χ694-44-44-44-44-44-444-4-4000000-2-22-22-22-22-2222-22-21-11-111-1-1−2323−232300003−33−33−33−3000000000000000000000000000000000000
χ704-44-4-44-444-44-4-4-4440000004-2-44-4-42-222-24-2-442-22-2222-2-20000000000000000000000000000000000000000000000000000
χ714-44-4-44-444-44-4-4-444000000-242-222-44-4-44-242-2-4-22-2222-2-20000000000000000000000000000000000000000000000000000
χ724-44-4-44-444-44-4-4-444000000-2-22-2222-222-2-2-22-221-11-1-1-111000000003-33-3-33-33000000000000000000000000000000000000
χ734-44-4-44-444-44-4-4-444000000-2-22-2222-222-2-2-22-221-11-1-1-11100000000-33-333-33-3000000000000000000000000000000000000
χ744-4-444-4-444-4-444-44-44i−4i4i4i−4i−4i-2-222-2-222-2-2-2222-221-1-111-11-1−2i2i2i−2i−2i2i−2i2ii−i−iii−i−ii000000000000000000000000000000000000
χ754-4-444-4-444-4-444-44-4−4i4i−4i−4i4i4i-2-222-2-222-2-2-2222-221-1-111-11-12i−2i−2i2i2i−2i2i−2i−iii−i−iii−i000000000000000000000000000000000000
χ764-4-44-444-44-4-44-44-44000000-2422-22-4-44-4-4-24-224-222-22-22-20000000000000000000000000000000000000000000000000000
χ774-4-44-444-44-4-44-44-44000000-2-222-2222-222-2-2-22-21-1-11-11-110000−2i32i32i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ784-4-44-444-44-4-44-44-44000000-2-222-2222-222-2-2-22-21-1-11-11-1100002i3−2i3−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000022002200000000-1-1-1-1-1-1-1-1000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000-2-200-2-20000000011111111000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000002200-2-2000000001111-1-1-1-1000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000-2-2002200000000-1-1-1-11111000000000000
χ8366-6-6-6-666-3-3333-3-330033−3333−3300000000000000000000000000000000000000000000002-200000000-1-1113−33−3000000000000
χ8466-6-6-6-666-3-3333-3-330033−3333−330000000000000000000000000000000000000000000000-220000000011-1-1−33−33000000000000
χ8566-6-6-6-666-3-3333-3-3300−3333−333300000000000000000000000000000000000000000000002-200000000-1-111−33−33000000000000
χ8666-6-6-6-666-3-3333-3-3300−3333−33330000000000000000000000000000000000000000000000-220000000011-1-13−33−3000000000000
χ876-66-6-66-66-33-3333-3-300−3i33i33i3−3i30000000000000000000000000000000000000000002-2000000000000−i3i3−i3i3-1-111000000000000
χ886-66-6-66-66-33-3333-3-300−3i33i33i3−3i3000000000000000000000000000000000000000000-22000000000000i3−i3i3−i311-1-1000000000000
χ896-66-6-66-66-33-3333-3-3003i3−3i3−3i33i30000000000000000000000000000000000000000002-2000000000000i3−i3i3−i3-1-111000000000000
χ906-66-6-66-66-33-3333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000000000-22000000000000−i3i3−i3i311-1-1000000000000
χ916-6-666-6-66-333-3-33-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000−i3i3i3−i33−3−33000000000000
χ926-6-666-6-66-333-3-33-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000i3−i3−i3i3−333−3000000000000
χ936-6-666-6-66-333-3-33-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000−i3i3i3−i3−333−3000000000000
χ946-6-666-6-66-333-3-33-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000i3−i3−i3i33−3−33000000000000
χ9512121212-12-12-12-12-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-121212-12-12-6-666-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-1212-1212-12-66-66-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-121212-12-666-66-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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