Finite Group Databasebeta

← Group #13140111

Character table — Group #13140111

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ922222222222222222222222-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200000000-1-1-1-100000000-1-1-1-100000000
χ1022222222222222222222222-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000111100000000111100000000
χ112222222222222222222222-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000002200220000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-200-2-2000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-11111-2-2-2-21111111122-2-200000000-1-1-1-100000000111100000000
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-1-12-12-1-1-1-1-1-1-1-11111-2-2-2-211111111-2-22200000000111100000000-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000002200-2-20000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-1222222-12-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000-2-2002200000000000000001111-1-1-1-1
χ172222-2-2-2-22222-2-2-2-200000022222-2-2222-2-2-2-2-2-22222-2-2-2-200000000000000002-2000000000022-2-200000000000000000000
χ182222-2-2-2-22222-2-2-2-200000022222-2-2222-2-2-2-2-2-22222-2-2-2-20000000000000000-220000000000-2-22200000000000000000000
χ192222-2-2-2-22222-2-2-2-20000002-1222-2-2-1-1-1111-21-2-1-1-1-1111133−3−300003333−3−3−3−32-20000000000-1-1110000000033−3−300000000
χ202222-2-2-2-22222-2-2-2-20000002-1222-2-2-1-1-1111-21-2-1-1-1-1111133−3−300003333−3−3−3−3-22000000000011-1-100000000−3−33300000000
χ212222-2-2-2-22222-2-2-2-20000002-1222-2-2-1-1-1111-21-2-1-1-1-11111−3−3330000−3−3−3−333332-20000000000-1-11100000000−3−33300000000
χ222222-2-2-2-22222-2-2-2-20000002-1222-2-2-1-1-1111-21-2-1-1-1-11111−3−3330000−3−3−3−33333-22000000000011-1-10000000033−3−300000000
χ2322-2-222-2-222-2-222-2-2000000222-2-22-22-2-22-2-222-222-2-222-2-2000000000000000000000000002i−2i000000000000000000002i2i−2i−2i
χ2422-2-222-2-222-2-222-2-2000000222-2-22-22-2-22-2-222-222-2-222-2-200000000000000000000000000−2i2i00000000000000000000−2i−2i2i2i
χ2522-2-222-2-222-2-222-2-2000000-12-111-112-2-22-2-2-121-1-111-1-111000033−3−333−3−333−3−300000000002i−2i0000000000000000−i3−i3i3i3−i−iii
χ2622-2-222-2-222-2-222-2-2000000-12-111-112-2-22-2-2-121-1-111-1-111000033−3−333−3−333−3−30000000000−2i2i0000000000000000i3i3−i3−i3ii−i−i
χ2722-2-222-2-222-2-222-2-2000000-12-111-112-2-22-2-2-121-1-111-1-1110000−3−333−3−333−3−33300000000002i−2i0000000000000000i3i3−i3−i3−i−iii
χ2822-2-222-2-222-2-222-2-2000000-12-111-112-2-22-2-2-121-1-111-1-1110000−3−333−3−333−3−3330000000000−2i2i0000000000000000−i3−i3i3i3ii−i−i
χ2922-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-222-2-2222-2-2-2-222000000000000000000002-2000000000022-2-20000000000000000
χ3022-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-222-2-2222-2-2-2-22200000000000000000000-220000000000-2-2220000000000000000
χ312-22-22-22-22-22-22-22-200000022-22-222-22-2-22-2-22-22-22-22-22-20000000000000000000000002i−2i00000000002i2i−2i−2i000000000000
χ322-22-22-22-22-22-22-22-200000022-22-222-22-2-22-2-22-22-22-22-22-2000000000000000000000000−2i2i0000000000−2i−2i2i2i000000000000
χ332-22-2-22-222-22-2-22-2200000022-22-2-2-2-22-22-222-222-22-2-22-2200000000000000000000002-2000000000000000000002-22-20000
χ342-22-2-22-222-22-2-22-2200000022-22-2-2-2-22-22-222-222-22-2-22-220000000000000000000000-2200000000000000000000-22-220000
χ352-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-2-1-11-111-11-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000002-200000000000000000000-11-11−i3i3−i3i3
χ362-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-2-1-11-111-11-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000-22000000000000000000001-11-1i3−i3i3−i3
χ372-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-2-1-11-111-11-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000002-200000000000000000000-11-11i3−i3i3−i3
χ382-22-2-22-222-22-2-22-22000000-121-1111-22-22-22-1-2-1-11-111-11-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000-22000000000000000000001-11-1−i3i3−i3i3
χ392-2-222-2-222-2-222-2-2200000022-2-222-2-2-22-2-22-2222-2-222-2-220000000000000000002-2000000000000000000002-22-200000000
χ402-2-222-2-222-2-222-2-2200000022-2-222-2-2-22-2-22-2222-2-222-2-22000000000000000000-2200000000000000000000-22-2200000000
χ412-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-2-12-111-1-111-1−i3i3−i3i30000−i3i3i3−i3i3−i3−i3i3002-200000000−i3i3−i3i300000000-11-1100000000
χ422-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-2-12-111-1-111-1−i3i3−i3i30000−i3i3i3−i3i3−i3−i3i300-2200000000i3−i3i3−i3000000001-11-100000000
χ432-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-2-12-111-1-111-1i3−i3i3−i30000i3−i3−i3i3−i3i3i3−i3002-200000000i3−i3i3−i300000000-11-1100000000
χ442-2-222-2-222-2-222-2-220000002-1-2-222-211-111-1-2-12-111-1-111-1i3−i3i3−i30000i3−i3−i3i3−i3i3i3−i300-2200000000−i3i3−i3i3000000001-11-100000000
χ452-2-22-222-22-2-22-222-22i−2i2i2i−2i−2i22-2-22-22-2-2222-22-2-22-2-22-222-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ462-2-22-222-22-2-22-222-22i−2i2i2i−2i−2i2-1-2-22-2211-1-1-1121-2-111-11-1-11−iii−i2i−2i−2i2i−iii−i−iii−i000000000000−i3i3i3−i3000000003−3−3300000000
χ472-2-22-222-22-2-22-222-22i−2i2i2i−2i−2i2-1-2-22-2211-1-1-1121-2-111-11-1-11−iii−i2i−2i−2i2i−iii−i−iii−i000000000000i3−i3−i3i300000000−333−300000000
χ482-2-22-222-22-2-22-222-22i−2i2i2i−2i−2i-1211-11-1-2-2222-2-1-21-111-11-1-112i−2i−2i2i−iii−i−iii−i−iii−i0000000000000000000000000000−i3i3i3−i33−3−33
χ492-2-22-222-22-2-22-222-22i−2i2i2i−2i−2i-1211-11-1-2-2222-2-1-21-111-11-1-112i−2i−2i2i−iii−i−iii−i−iii−i0000000000000000000000000000i3−i3−i3i3−333−3
χ502-2-22-222-22-2-22-222-2−2i2i−2i−2i2i2i22-2-22-22-2-2222-22-2-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ512-2-22-222-22-2-22-222-2−2i2i−2i−2i2i2i2-1-2-22-2211-1-1-1121-2-111-11-1-11i−i−ii−2i2i2i−2ii−i−iii−i−ii000000000000−i3i3i3−i300000000−333−300000000
χ522-2-22-222-22-2-22-222-2−2i2i−2i−2i2i2i2-1-2-22-2211-1-1-1121-2-111-11-1-11i−i−ii−2i2i2i−2ii−i−iii−i−ii000000000000i3−i3−i3i3000000003−3−3300000000
χ532-2-22-222-22-2-22-222-2−2i2i−2i−2i2i2i-1211-11-1-2-2222-2-1-21-111-11-1-11−2i2i2i−2ii−i−iii−i−iii−i−ii0000000000000000000000000000−i3i3i3−i3−333−3
χ542-2-22-222-22-2-22-222-2−2i2i−2i−2i2i2i-1211-11-1-2-2222-2-1-21-111-11-1-11−2i2i2i−2ii−i−iii−i−iii−i−ii0000000000000000000000000000i3−i3−i3i33−3−33
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
χ574444-4-4-4-44444-4-4-4-4000000-24-2-2-222444-4-4-42-42-2-2-2-222220000000000000000000000000000000000000000000000000000
χ584444-4-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-2-22222221111-1-1-1-12323−23−230000−3−3−3−33333000000000000000000000000000000000000
χ594444-4-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-2-22222221111-1-1-1-1−23−23232300003333−3−3−3−3000000000000000000000000000000000000
χ6044-4-444-4-444-4-444-4-40000004-24-4-44-4-222-2224-2-4-2-222-2-2220000000000000000000000000000000000000000000000000000
χ6144-4-444-4-444-4-444-4-4000000-2-2-222-22-222-222-2-2211-1-111-1-100002323−23−23−3−333−3−333000000000000000000000000000000000000
χ6244-4-444-4-444-4-444-4-4000000-2-2-222-22-222-222-2-2211-1-111-1-10000−23−23232333−3−333−3−3000000000000000000000000000000000000
χ6344-4-4-4-44444-4-4-4-4440000004-24-4-4-44-2222-2-2-424-2-22222-2-20000000000000000000000000000000000000000000000000000
χ6444-4-4-4-44444-4-4-4-444000000-24-2222-24-4-4-4442-4-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ6544-4-4-4-44444-4-4-4-444000000-2-2-2222-2-2222-2-222-211-1-1-1-1110000000033-3-3-3-333000000000000000000000000000000000000
χ6644-4-4-4-44444-4-4-4-444000000-2-2-2222-2-2222-2-222-211-1-1-1-11100000000-3-33333-3-3000000000000000000000000000000000000
χ674-44-44-44-44-44-44-44-40000004-2-44-4442-222-22-4-2-4-22-22-22-220000000000000000000000000000000000000000000000000000
χ684-44-44-44-44-44-44-44-4000000-242-22-2-2-44-4-44-4242-22-22-22-220000000000000000000000000000000000000000000000000000
χ694-44-44-44-44-44-44-44-4000000-2-22-22-2-22-222-222-221-11-11-11-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ704-44-44-44-44-44-44-44-4000000-2-22-22-2-22-222-222-221-11-11-11-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ714-44-4-44-444-44-4-44-440000004-2-44-4-4-42-22-22-2424-22-222-22-20000000000000000000000000000000000000000000000000000
χ724-44-4-44-444-44-4-44-44000000-2-22-22222-22-22-2-22-21-11-1-11-110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ734-44-4-44-444-44-4-44-44000000-2-22-22222-22-22-2-22-21-11-1-11-1100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ744-4-444-4-444-4-444-4-44000000-2422-2-22-4-44-4-4424-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ754-4-444-4-444-4-444-4-44000000-2-222-2-2222-222-22-2-21-1-111-1-11−2i32i3−2i32i30000i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ764-4-444-4-444-4-444-4-44000000-2-222-2-2222-222-22-2-21-1-111-1-112i3−2i32i3−2i30000−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ774-4-44-444-44-4-44-444-44i−4i4i4i−4i−4i-2-222-22-222-2-2-22-2221-1-11-111-1−2i2i2i−2i−2i2i2i−2ii−i−iii−i−ii000000000000000000000000000000000000
χ784-4-44-444-44-4-44-444-4−4i4i−4i−4i4i4i-2-222-22-222-2-2-22-2221-1-11-111-12i−2i−2i2i2i−2i−2i2i−iii−i−iii−i000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000220022000000-1-1-1-1-1-1-1-1000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-200-2-200000011111111000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000002200-2-2000000-1-1-1-11111000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-200220000001111-1-1-1-1000000000000
χ8366-6-6-6-666-3-33333-3-300−3i33i3−3i33i3000000000000000000000000000000000000000000002-20000000000-1-111−i3i3−i3i3000000000000
χ8466-6-6-6-666-3-33333-3-300−3i33i3−3i33i300000000000000000000000000000000000000000000-22000000000011-1-1i3−i3i3−i3000000000000
χ8566-6-6-6-666-3-33333-3-3003i3−3i33i3−3i3000000000000000000000000000000000000000000002-20000000000-1-111i3−i3i3−i3000000000000
χ8666-6-6-6-666-3-33333-3-3003i3−3i33i3−3i300000000000000000000000000000000000000000000-22000000000011-1-1−i3i3−i3i3000000000000
χ876-66-66-66-6-33-33-33-330033−33−33330000000000000000000000000000000000000000000000002i−2i000000−i3i3−i3i3−i−iii000000000000
χ886-66-66-66-6-33-33-33-330033−33−3333000000000000000000000000000000000000000000000000−2i2i000000i3−i3i3−i3ii−i−i000000000000
χ896-66-66-66-6-33-33-33-3300−333333−330000000000000000000000000000000000000000000000002i−2i000000i3−i3i3−i3−i−iii000000000000
χ906-66-66-66-6-33-33-33-3300−333333−33000000000000000000000000000000000000000000000000−2i2i000000−i3i3−i3i3ii−i−i000000000000
χ916-6-66-666-6-333-33-3-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000−i3i3i3−i33−3−33000000000000
χ926-6-66-666-6-333-33-3-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000i3−i3−i3i3−333−3000000000000
χ936-6-66-666-6-333-33-3-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000−i3i3i3−i3−333−3000000000000
χ946-6-66-666-6-333-33-3-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000i3−i3−i3i33−3−33000000000000
χ9512121212-12-12-12-12-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-121212-12-12-6-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000
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).