Finite Group Databasebeta

← Group #13141171

Character table — Group #13141171

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666226666336666666666666636666666666666666666666622444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ922222222222222222222222-122222-1-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002200220000000000000000-1-1-1-1-1-1-1-1
χ1022222222222222222222222-122222-1-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-2-200-2-2000000000000000011111111
χ112222222222222222222222-12-1-1-1-1-122222-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100222200000000000000-1-1-1-1-1-1-1-100000000
χ122222222222222222222222-12-1-1-1-1-122222-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2000000000000001111111100000000
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-122-1-1-1-2-2-2-21111-1-1-1-1-1-1-1111111110000002200-2-20000000000000000-1-1-1-11111
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-122-1-1-1-2-2-2-21111-1-1-1-1-1-1-111111111000000-2-2002200000000000000001111-1-1-1-1
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-1-122-11111-2-2-2-2-1-1-1-1-1-1-1111111110022-2-200000000000000-1-1-1-1111100000000
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-1-122-11111-2-2-2-2-1-1-1-1-1-1-11111111100-2-222000000000000001111-1-1-1-100000000
χ17222-22-2-2-22222-2-2-2-200000022222-2-222-2-2-2-2-22-2200000000222-2-2-2-20000000000002i−2i0000000000000000002i2i−2i−2i00000000
χ18222-22-2-2-22222-2-2-2-200000022222-2-222-2-2-2-2-22-2200000000222-2-2-2-2000000000000−2i2i000000000000000000−2i−2i2i2i00000000
χ19222-22-2-2-22222-2-2-2-2000000-12-1-1-11122-2-2-2112-2-1−i3−i3i3i30000-1-1-11111−i3−i3−i3−i3i3i3i3i300002i−2i0000000000000033−3−3−i−iii00000000
χ20222-22-2-2-22222-2-2-2-2000000-12-1-1-11122-2-2-2112-2-1−i3−i3i3i30000-1-1-11111−i3−i3−i3−i3i3i3i3i30000−2i2i00000000000000−3−333ii−i−i00000000
χ21222-22-2-2-22222-2-2-2-2000000-12-1-1-11122-2-2-2112-2-1i3i3−i3−i30000-1-1-11111i3i3i3i3−i3−i3−i3−i300002i−2i00000000000000−3−333−i−iii00000000
χ22222-22-2-2-22222-2-2-2-2000000-12-1-1-11122-2-2-2112-2-1i3i3−i3−i30000-1-1-11111i3i3i3i3−i3−i3−i3−i30000−2i2i0000000000000033−3−3ii−i−i00000000
χ2322-22-22-2-222-2-222-2-2000000222-2-22-22-222-22-2-2-22000000002-2-222-2-20000000000000000002i−2i000000000000000000002i2i−2i−2i
χ2422-22-22-2-222-2-222-2-2000000222-2-22-22-222-22-2-2-22000000002-2-222-2-2000000000000000000−2i2i00000000000000000000−2i−2i2i2i
χ2522-22-22-2-222-2-222-2-20000002-12-2-22-2-11-1-112-211-10000−i3−i3i3i3-111-1-111−i3−i3i3i3−i3−i3i3i300000000002i−2i000000000000000033−3−3−i−iii
χ2622-22-22-2-222-2-222-2-20000002-12-2-22-2-11-1-112-211-10000−i3−i3i3i3-111-1-111−i3−i3i3i3−i3−i3i3i30000000000−2i2i0000000000000000−3−333ii−i−i
χ2722-22-22-2-222-2-222-2-20000002-12-2-22-2-11-1-112-211-10000i3i3−i3−i3-111-1-111i3i3−i3−i3i3i3−i3−i300000000002i−2i0000000000000000−3−333−i−iii
χ2822-22-22-2-222-2-222-2-20000002-12-2-22-2-11-1-112-211-10000i3i3−i3−i3-111-1-111i3i3−i3−i3i3i3−i3−i30000000000−2i2i000000000000000033−3−3ii−i−i
χ2922-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-22-22-222000000002-2-2-2-222000000002-2000000000022-2-200000000000000000000
χ3022-2-2-2-22222-2-2-2-222000000222-2-2-222-2-2-22-22-222000000002-2-2-2-22200000000-220000000000-2-22200000000000000000000
χ312-222-2-22-22-22-22-22-200000022-22-22-2-222-22-22-2-2200000000-22-22-22-2000000000000002i−2i000000000000000000002i−2i2i−2i0000
χ322-222-2-22-22-22-22-22-200000022-22-22-2-222-22-22-2-2200000000-22-22-22-200000000000000−2i2i00000000000000000000−2i2i−2i2i0000
χ332-222-2-22-22-22-22-22-20000002-1-22-22-21-1-11-1-2211-10000−i3i3−i3i31-11-11-11−i3i3−i3i3−i3i3−i3i30000002i−2i00000000000000000000−ii−ii3−33−3
χ342-222-2-22-22-22-22-22-20000002-1-22-22-21-1-11-1-2211-10000−i3i3−i3i31-11-11-11−i3i3−i3i3−i3i3−i3i3000000−2i2i00000000000000000000i−ii−i−33−33
χ352-222-2-22-22-22-22-22-20000002-1-22-22-21-1-11-1-2211-10000i3−i3i3−i31-11-11-11i3−i3i3−i3i3−i3i3−i30000002i−2i00000000000000000000−ii−ii−33−33
χ362-222-2-22-22-22-22-22-20000002-1-22-22-21-1-11-1-2211-10000i3−i3i3−i31-11-11-11i3−i3i3−i3i3−i3i3−i3000000−2i2i00000000000000000000i−ii−i3−33−3
χ372-22-2-22-222-22-2-22-2200000022-22-2-22-22-22-22-2-22200000000-22-2-22-2200000000000000002-200000022-2-20000000000000000
χ382-22-2-22-222-22-2-22-2200000022-22-2-22-22-22-22-2-22200000000-22-2-22-220000000000000000-22000000-2-2220000000000000000
χ392-2-222-2-222-2-222-2-222-222-2-222-2-2222-2-22-2-2-2-22222-22-22-2-22-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ402-2-222-2-222-2-222-2-222-222-2-22-1-2-222211-111-2-2-1-1-12-22-2-111-111-1-111-1-111-1-111-10000000000000000000000000000−i3i3i3−i3−i3i3i3−i3
χ412-2-222-2-222-2-222-2-222-222-2-22-1-2-222211-111-2-2-1-1-12-22-2-111-111-1-111-1-111-1-111-10000000000000000000000000000i3−i3−i3i3i3−i3−i3i3
χ422-2-222-2-222-2-222-2-222-222-2-2-1211-1-1-1-2-22-2-21122-1-11-112-2-2211-1-111-1-111-1-111-1000000000000000000003−33−33−33−300000000
χ432-2-222-2-222-2-222-2-222-222-2-2-1211-1-1-1-2-22-2-21122-1-11-112-2-2211-1-111-1-111-1-111-100000000000000000000−33−33−33−3300000000
χ442-2-222-2-222-2-222-2-22-22-2-22222-2-2222-2-22-2-2-2-2222-22-22-222-2-2-222-2-22-222-2-222-2000000000000000000000000000000000000
χ452-2-222-2-222-2-222-2-22-22-2-2222-1-2-222211-111-2-2-1-1-1-22-221-1-1111-1-111-11-1-111-1-110000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ462-2-222-2-222-2-222-2-22-22-2-2222-1-2-222211-111-2-2-1-1-1-22-221-1-1111-1-111-11-1-111-1-110000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ472-2-222-2-222-2-222-2-22-22-2-222-1211-1-1-1-2-22-2-21122-11-11-1-222-211-1-111-11-1-111-1-11000000000000000000003−33−3−33−3300000000
χ482-2-222-2-222-2-222-2-22-22-2-222-1211-1-1-1-2-22-2-21122-11-11-1-222-211-1-111-11-1-111-1-1100000000000000000000−33−333−33−300000000
χ492-2-2-2222-22-2-22-222-200000022-2-22-2-2-2-2-222222-2200000000-2-22-222-200000000002-200000000000000002-2-22000000000000
χ502-2-2-2222-22-2-22-222-200000022-2-22-2-2-2-2-222222-2200000000-2-22-222-20000000000-220000000000000000-222-2000000000000
χ512-2-2-2222-22-2-22-222-2000000-1211-111-2-2-222-1-12-2-1−i3i3i3−i3000011-11-1-11−i3i3i3−i3i3−i3−i3i3002-20000000000000000-111-1−i3i3i3−i300000000
χ522-2-2-2222-22-2-22-222-2000000-1211-111-2-2-222-1-12-2-1−i3i3i3−i3000011-11-1-11−i3i3i3−i3i3−i3−i3i300-2200000000000000001-1-11i3−i3−i3i300000000
χ532-2-2-2222-22-2-22-222-2000000-1211-111-2-2-222-1-12-2-1i3−i3−i3i3000011-11-1-11i3−i3−i3i3−i3i3i3−i3002-20000000000000000-111-1i3−i3−i3i300000000
χ542-2-2-2222-22-2-22-222-2000000-1211-111-2-2-222-1-12-2-1i3−i3−i3i3000011-11-1-11i3−i3−i3i3−i3i3i3−i300-2200000000000000001-1-11−i3i3i3−i300000000
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
χ57444-44-4-4-44444-4-4-4-40000004-2444-4-4-2-2222-4-4-22-200000000-2-2-2222200000000000000000000000000000000000000000000
χ58444-44-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-222222-221−2i3−2i32i32i30000111-1-1-1-1i3i3i3i3−i3−i3−i3−i3000000000000000000000000000000000000
χ59444-44-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-222222-2212i32i3−2i3−2i30000111-1-1-1-1−i3−i3−i3−i3i3i3i3i3000000000000000000000000000000000000
χ6044-44-44-4-444-4-444-4-4000000-24-222-224-444-4-22-4-4-200000000-222-2-22200000000000000000000000000000000000000000000
χ6144-44-44-4-444-4-444-4-4000000-2-2-222-22-22-2-22-222210000−2i3−2i32i32i31-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ6244-44-44-4-444-4-444-4-4000000-2-2-222-22-22-2-22-2222100002i32i3−2i3−2i31-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ6344-4-4-4-44444-4-4-4-4440000004-24-4-4-44-2222-2-442-2-200000000-22222-2-200000000000000000000000000000000000000000000
χ6444-4-4-4-44444-4-4-4-444000000-24-2222-24-4-4-442-2-44-200000000-22222-2-200000000000000000000000000000000000000000000
χ6544-4-4-4-44444-4-4-4-444000000-2-2-2222-2-2222-22-22-21000000001-1-1-1-11133-3-3-3-333000000000000000000000000000000000000
χ6644-4-4-4-44444-4-4-4-444000000-2-2-2222-2-2222-22-22-21000000001-1-1-1-111-3-33333-3-3000000000000000000000000000000000000
χ674-444-4-44-44-44-44-44-4000000-242-22-22-444-442-2-4-4-2000000002-22-22-2200000000000000000000000000000000000000000000
χ684-444-4-44-44-44-44-44-4000000-2-22-22-222-2-22-22-22210000−2i32i3−2i32i3-11-11-11-1i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ694-444-4-44-44-44-44-44-4000000-2-22-22-222-2-22-22-222100002i3−2i32i3−2i3-11-11-11-1−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ704-44-4-44-444-44-4-44-440000004-2-44-4-442-22-224-42-2-2000000002-222-22-200000000000000000000000000000000000000000000
χ714-44-4-44-444-44-4-44-44000000-242-222-2-44-44-4-22-44-2000000002-222-22-200000000000000000000000000000000000000000000
χ724-44-4-44-444-44-4-44-44000000-2-22-222-22-22-22-222-2100000000-11-1-11-113-33-3-33-33000000000000000000000000000000000000
χ734-44-4-44-444-44-4-44-44000000-2-22-222-22-22-22-222-2100000000-11-1-11-11-33-333-33-3000000000000000000000000000000000000
χ744-4-444-4-444-4-444-4-444-444-4-4-2-222-2-2-222-22222-2-21-22-22-222-2-1-111-1-111-1-111-1-11000000000000000000000000000000000000
χ754-4-444-4-444-4-444-4-44-44-4-444-2-222-2-2-222-22222-2-212-22-22-2-22-1-111-1-11-111-1-111-1000000000000000000000000000000000000
χ764-4-4-4444-44-4-44-444-40000004-2-4-44-4-4222-2-244-22-20000000022-22-2-2200000000000000000000000000000000000000000000
χ774-4-4-4444-44-4-44-444-4000000-2-222-222222-2-2-2-2-221−2i32i32i3−2i30000-1-11-111-1i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ784-4-4-4444-44-4-44-444-4000000-2-222-222222-2-2-2-2-2212i3−2i3−2i32i30000-1-11-111-1−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000220000002200-1-1-1-1-1-1-1-10000000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-2000000-2-200111111110000000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000022000000-2-200-1-1-1-111110000000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-200000022001111-1-1-1-10000000000000000
χ8366-6-6-6-666-3-33333-3-300−3i33i3−3i33i300000000000000000000000000000000000000002-20000000000-1-111−i3i3−i3i30000000000000000
χ8466-6-6-6-666-3-33333-3-300−3i33i3−3i33i30000000000000000000000000000000000000000-22000000000011-1-1i3−i3i3−i30000000000000000
χ8566-6-6-6-666-3-33333-3-3003i3−3i33i3−3i300000000000000000000000000000000000000002-20000000000-1-111i3−i3i3−i30000000000000000
χ8666-6-6-6-666-3-33333-3-3003i3−3i33i3−3i30000000000000000000000000000000000000000-22000000000011-1-1−i3i3−i3i30000000000000000
χ876-66-6-66-66-33-333-33-300−3i33i33i3−3i30000000000000000000000000000000000000000000000002-200−i3i3−i3i3-1-1110000000000000000
χ886-66-6-66-66-33-333-33-300−3i33i33i3−3i3000000000000000000000000000000000000000000000000-2200i3−i3i3−i311-1-10000000000000000
χ896-66-6-66-66-33-333-33-3003i3−3i3−3i33i30000000000000000000000000000000000000000000000002-200i3−i3i3−i3-1-1110000000000000000
χ906-66-6-66-66-33-333-33-3003i3−3i3−3i33i3000000000000000000000000000000000000000000000000-2200−i3i3−i3i311-1-10000000000000000
χ916-6-666-6-66-333-3-333-36-6-3-3330000000000000000000000000000000000000000000000000000−i3i3i3−i3−i3i3i3−i30000000000000000
χ926-6-666-6-66-333-3-333-36-6-3-3330000000000000000000000000000000000000000000000000000i3−i3−i3i3i3−i3−i3i30000000000000000
χ936-6-666-6-66-333-3-333-3-6633-3-30000000000000000000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i30000000000000000
χ946-6-666-6-66-333-3-333-3-6633-3-30000000000000000000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i30000000000000000
χ95121212-1212-12-12-12-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-1212-1212-12-12-6-666-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-121212-12-1212-12-66-66-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-12-12121212-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000

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