Finite Group Databasebeta

← Group #13150684

Character table — Group #13150684

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222223446661212121246612123366666666663666666666121212121212121212121212121212122222444422244444666666666612121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-11-11-1-1-11111-1-1-1-111-1-1111-11-1
χ61111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-11-11111111-1-1-1-1-1-111-1-1-11-11
χ71111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-11-11-1-1-1-1-1-1111111-1-111-11-11
χ81111111-1-1111-1-1-1-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-11-111-1-1-1-11111-1-111-1-11-11-1
χ91111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1111-1-1-1-111-1-111-1-11111-1-111-1-1
χ101111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-111-1-11-1-1-1111111-1-111-1-1-1-1-1-111-1-111
χ111111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-11-1-111-1-1-1-111-1-1111111-1-1-1-111
χ121111-1-11111111111-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-111-1-1-1-11111-1-1
χ131111-1-11-1-1111-1-1-1-11-1-11111111-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-111-1-1-111-11-1-111111-1-1-1-11111-1-1-1-11-1-11
χ141111-1-11-1-1111-1-1-1-11-1-11111111-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1-111-11-11-111-1-1-111-1-1-1-111-1-11111-111-1
χ151111-1-11-1-1111-1-1-1-11-1-11111111-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-11111-1-11-11-1-111-111-1-11111-1-111-1-1-1-1-111-1
χ161111-1-11-1-1111-1-1-1-11-1-11111111-1-1-1-11111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111-1-1111-1-111-1-11-1-1-1-11111-1-1-1-111111-1-11
χ172222222222222222222222-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200002200000000-1-1-1-1-1-1-1-10000000000
χ182222222222222222222222-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000-2-200000000111111110000000000
χ19222222222222222222222-12-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000022220000000000000000-1-1-1-1
χ20222222222222222222222-12-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000000001111
χ212222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-11111-2-2-2-21111111122-2-200002-200000000-1-1-1-111110000000000
χ222222222-2-2222-2-2-2-2-222-2-22-12-1-1-1-1-1-1-122-122-1-1-1-1-1-1-11111-2-2-2-211111111-2-2220000-22000000001111-1-1-1-10000000000
χ232222222-2-2222-2-2-2-2-222-2-2-12-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000000002-22-20000000000000000-11-11
χ242222222-2-2222-2-2-2-2-222-2-2-12-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000-22-2200000000000000001-11-1
χ252222-2-22222222222-2-2-2-2-22-12-1-11111-122-1-2-2-1-11111-1-1-11122-2-2-1-1-1-1111122220000-2-200000000-1-111-1-1110000000000
χ262222-2-22222222222-2-2-2-2-22-12-1-11111-122-1-2-2-1-11111-1-1-11122-2-2-1-1-1-11111-2-2-2-20000220000000011-1-111-1-10000000000
χ272222-2-22222222222-2-2-2-2-2-12-122-2-2-2-22-1-1-111-1-11111-122-2-2-1-111-1-1-1-1111100000000000022-2-20000000000000000-1-111
χ282222-2-22222222222-2-2-2-2-2-12-122-2-2-2-22-1-1-111-1-11111-122-2-2-1-111-1-1-1-11111000000000000-2-222000000000000000011-1-1
χ292222-2-22-2-2222-2-2-2-22-2-2222-12-1-11111-122-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-122-2-20000-2200000000-1-11111-1-10000000000
χ302222-2-22-2-2222-2-2-2-22-2-2222-12-1-11111-122-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-1-2-22200002-20000000011-1-1-1-1110000000000
χ312222-2-22-2-2222-2-2-2-22-2-222-12-122-2-2-2-22-1-1-111-1-11111-1-2-22211-1-11111-1-1-1-10000000000002-2-220000000000000000-111-1
χ322222-2-22-2-2222-2-2-2-22-2-222-12-122-2-2-2-22-1-1-111-1-11111-1-2-22211-1-11111-1-1-1-1000000000000-222-200000000000000001-1-11
χ3322-2-22-22002-2-2000002-2002222-222-2-2-2-2-222-22-222-2-2-2000000000000000000002i−2i2i−2i0000000000000000002i−2i002i−2i0000
χ3422-2-22-22002-2-2000002-2002222-222-2-2-2-2-222-22-222-2-2-200000000000000000000−2i2i−2i2i000000000000000000−2i2i00−2i2i0000
χ3522-2-2-222002-2-200000-22002222-2-2-222-2-2-22-222-2-2-222-2000000000000000000002i−2i−2i2i0000000000000000002i−2i00−2i2i0000
χ3622-2-2-222002-2-200000-22002222-2-2-222-2-2-22-222-2-2-222-200000000000000000000−2i2i2i−2i000000000000000000−2i2i002i−2i0000
χ372-2-220022-2-2-2222-2-20000022-2-2-200002-22200-2-2000022-2002-20022-2-200002-22-2000000000000002-2002-2000000000000
χ382-2-220022-2-2-2222-2-20000022-2-2-200002-22200-2-2000022-2002-20022-2-20000-22-2200000000000000-2200-22000000000000
χ392-2-220022-2-2-2222-2-2000002-1-211−i3i3−i3i3-1-22-10011−i3i3−i3i3-1-11−i3i32-200-1-111−i3−i3i3i32-22-200000000000000-11−i3i3-11−i3i30000000000
χ402-2-220022-2-2-2222-2-2000002-1-211−i3i3−i3i3-1-22-10011−i3i3−i3i3-1-11−i3i32-200-1-111−i3−i3i3i3-22-22000000000000001-1i3−i31-1i3−i30000000000
χ412-2-220022-2-2-2222-2-2000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-1-11i3−i32-200-1-111i3i3−i3−i32-22-200000000000000-11i3−i3-11i3−i30000000000
χ422-2-220022-2-2-2222-2-2000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-1-11i3−i32-200-1-111i3i3−i3−i3-22-22000000000000001-1−i3i31-1−i3i30000000000
χ432-2-22002-22-2-22-2-2220000022-2-2-200002-22200-2-200002-2200-2200-2-22200002-2-22000000000000002-200-22000000000000
χ442-2-22002-22-2-22-2-2220000022-2-2-200002-22200-2-200002-2200-2200-2-2220000-222-200000000000000-22002-2000000000000
χ452-2-22002-22-2-22-2-222000002-1-211−i3i3−i3i3-1-22-10011−i3i3−i3i3-11-1i3−i3-220011-1-1i3i3−i3−i32-2-2200000000000000-11−i3i31-1i3−i30000000000
χ462-2-22002-22-2-22-2-222000002-1-211−i3i3−i3i3-1-22-10011−i3i3−i3i3-11-1i3−i3-220011-1-1i3i3−i3−i3-222-2000000000000001-1i3−i3-11−i3i30000000000
χ472-2-22002-22-2-22-2-222000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-11-1−i3i3-220011-1-1−i3−i3i3i32-2-2200000000000000-11i3−i31-1−i3i30000000000
χ482-2-22002-22-2-22-2-222000002-1-211i3−i3i3−i3-1-22-10011i3−i3i3−i3-11-1−i3i3-220011-1-1−i3−i3i3i3-222-2000000000000001-1−i3i3-11i3−i30000000000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ504444444-4-4444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ514444-4-44444444444-4-4-4-4-4-2-2-2-2-22222-2-2-212211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000000000
χ524444-4-44-4-4444-4-4-4-44-4-444-2-2-2-2-22222-2-2-212211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5344-4-44-44004-4-4000004-4004-24-22-2-2222-4-4-24-4-22-2-22220000000000000000000000000000000000000000000000000000
χ5444-4-44-44004-4-4000004-400-24-24-444-4-4-422-2-22-22-2-22220000000000000000000000000000000000000000000000000000
χ5544-4-44-44004-4-4000004-400-2-2-2-22-2-2222221-221-111-1-1-1000000003i−3i3i−3i3i−3i3i−3i000000000000000000000000000000000000
χ5644-4-44-44004-4-4000004-400-2-2-2-22-2-2222221-221-111-1-1-100000000−3i3i−3i3i−3i3i−3i3i000000000000000000000000000000000000
χ5744-4-4-444004-4-400000-44004-24-2222-2-22-4-4-2-44-2222-2-220000000000000000000000000000000000000000000000000000
χ5844-4-4-444004-4-400000-4400-24-24-4-4-444-422-22-2-2222-2-220000000000000000000000000000000000000000000000000000
χ5944-4-4-444004-4-400000-4400-2-2-2-2222-2-222212-21-1-1-111-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ6044-4-4-444004-4-400000-4400-2-2-2-2222-2-222212-21-1-1-111-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ614-44-400400-44-400000000044-4-440000-44-4400-440000-40000000000000000000000000000000000000000000000000000
χ624-44-400400-44-40000000004-2-42-2−2i32i32i3−2i324-4-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000000000
χ634-44-400400-44-40000000004-2-42-22i3−2i3−2i32i324-4-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000000000
χ644-44-400400-44-4000000000-242-440000-4-22-2002-20000200000023−23000023−23−2323000000000000000000000000000000000000
χ654-44-400400-44-4000000000-242-440000-4-22-2002-200002000000−23230000−232323−23000000000000000000000000000000000000
χ664-44-400400-44-4000000000-2-222-2−2i32i32i3−2i32-22100-11i3−i3−i3i3-100000023−23−3i3i3i−3i−333−3000000000000000000000000000000000000
χ674-44-400400-44-4000000000-2-222-2−2i32i32i3−2i32-22100-11i3−i3−i3i3-1000000−23233i−3i−3i3i3−3−33000000000000000000000000000000000000
χ684-44-400400-44-4000000000-2-222-22i3−2i3−2i32i32-22100-11−i3i3i3−i3-100000023−233i−3i−3i3i−333−3000000000000000000000000000000000000
χ694-44-400400-44-4000000000-2-222-22i3−2i3−2i32i32-22100-11−i3i3i3−i3-1000000−2323−3i3i3i−3i3−3−33000000000000000000000000000000000000
χ704-4-440044-4-4-4444-4-400000-242-4-4000042-2-200220000-24-400-2200-2-2220000000000000000000000000000000000000000
χ714-4-440044-4-4-4444-4-400000-2-2222−2i32i3−2i32i3-22-2100-1-1i3−i3i3−i31-22−2i32i3-220011-1-1i3i3−i3−i3000000000000000000000000000000000000
χ724-4-440044-4-4-4444-4-400000-2-22222i3−2i32i3−2i3-22-2100-1-1−i3i3−i3i31-222i3−2i3-220011-1-1−i3−i3i3i3000000000000000000000000000000000000
χ734-4-44004-44-4-44-4-44400000-242-4-4000042-2-200220000-2-44002-20022-2-20000000000000000000000000000000000000000
χ744-4-44004-44-4-44-4-44400000-2-2222−2i32i3−2i32i3-22-2100-1-1i3−i3i3−i312-22i3−2i32-200-1-111−i3−i3i3i3000000000000000000000000000000000000
χ754-4-44004-44-4-44-4-44400000-2-22222i3−2i32i3−2i3-22-2100-1-1−i3i3−i3i312-2−2i32i32-200-1-111i3i3−i3−i3000000000000000000000000000000000000
χ76666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000222200220000-1-100000000-1-1-1-1-1-10000
χ77666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-200-2-2000011000000001111110000
χ78666666-3-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000222200-2-200001100000000-1-111-1-10000
χ79666666-3-6-6-3-3-33333-6-3-333000000000000000000000000000000000000000000-2-2-2-200220000-1-10000000011-1-1110000
χ806666-6-6-366-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-200-2200001100000000-1-1-1-1110000
χ816666-6-6-366-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222002-20000-1-1000000001111-1-10000
χ826666-6-6-3-6-6-3-3-33333633-3-300000000000000000000000000000000000000000022-2-2002-20000-1-100000000-1-111110000
χ836666-6-6-3-6-6-3-3-33333633-3-3000000000000000000000000000000000000000000-2-22200-220000110000000011-1-1-1-10000
χ8466-6-66-6-300-33333−3333−330-3333−330000000000000000000000000000000000000000002i−2i2i−2i00000000−i3i300000000−ii−i3i3−ii0000
χ8566-6-66-6-300-33333−3333−330-3333−33000000000000000000000000000000000000000000−2i2i−2i2i00000000i3−i300000000i−ii3−i3i−i0000
χ8666-6-66-6-300-333−3333−33330-33−33330000000000000000000000000000000000000000002i−2i2i−2i00000000i3−i300000000−iii3−i3−ii0000
χ8766-6-66-6-300-333−3333−33330-33−3333000000000000000000000000000000000000000000−2i2i−2i2i00000000−i3i300000000i−i−i3i3i−i0000
χ8866-6-6-66-300-33333−3333−3303-3−33330000000000000000000000000000000000000000002i−2i−2i2i00000000i3−i300000000−ii−i3i3i−i0000
χ8966-6-6-66-300-33333−3333−3303-3−3333000000000000000000000000000000000000000000−2i2i2i−2i00000000−i3i300000000i−ii3−i3−ii0000
χ9066-6-6-66-300-333−3333−333303-333−330000000000000000000000000000000000000000002i−2i−2i2i00000000−i3i300000000−iii3−i3i−i0000
χ9166-6-6-66-300-333−3333−333303-333−33000000000000000000000000000000000000000000−2i2i2i−2i00000000i3−i300000000i−i−i3i3−ii0000
χ9212-1212-1200-6006-6663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-1200-6006-66−636363−630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-612-1266-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-6-121266-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000

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