Finite Group Databasebeta

← Group #13157227

Character table — Group #13157227

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122224444444444444444444444444448888888888888888888888888888888888888881818181836363636727272108108108108108108108108
order12223666333333466666666666666666612122666666666666666666666666661212121212121212121212124444121212124121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-111-1-111-1-1
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-111-1-111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111ii−i−i−i−iii
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111−i−iiiii−i−i
χ922222222222222-2222222222222222222-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-200000000000
χ1022222222222222-2222222222222222222-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22200000000000
χ112222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12-1-100000000
χ122222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-21100000000
χ132222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-211-2-2-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-12222-1-1-1-1-21100000000
χ142222-1-1-1-122-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-211-2-2-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-2-2-2-211112-1-100000000
χ152222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110−i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-2-2-21111111122-2-2-1-1110−i3i300000000
χ162222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110−i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-2-2-211111111-2-22211-1-10i3−i300000000
χ172222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-2-2-21111111122-2-2-1-1110i3−i300000000
χ182222-1-1-1-122-1-1-1-1-22222-1-1-1-1-1-1-1-122-1-1-1-1110i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-2-2-211111111-2-22211-1-10−i3i300000000
χ1922-2-222-2-2222222022-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000002i−2i002i−2i0001+i−1−i001−i−1+i00
χ2022-2-222-2-2222222022-2-22222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000002i−2i002i−2i000−1−i1+i00−1+i1−i00
χ2122-2-222-2-2222222022-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000−2i2i00−2i2i0001−i−1+i001+i−1−i00
χ2222-2-222-2-2222222022-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000−2i2i00−2i2i000−1+i1−i00−1−i1+i00
χ232-22-22-22-22222220-2-222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000002i−2i002i−2i00000001+i−1−i001−i−1+i
χ242-22-22-22-22222220-2-222-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000002i−2i002i−2i0000000−1−i1+i00−1+i1−i
χ252-22-22-22-22222220-2-222-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000−2i2i00−2i2i00000001−i−1+i001+i−1−i
χ262-22-22-22-22222220-2-222-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000000−2i2i00−2i2i0000000−1+i1−i00−1−i1+i
χ27444444441-211-2-241-21-211-2-211-2-21-211-2-2444441111-2-2-2-21111-2-2-2-21111-2-2-2-211-2-21111-2-2-2-20000000000000000000
χ28444444441-211-2-241-21-211-2-211-2-21-211-2-244-4-4-4-1-1-1-12222-1-1-1-12222-1-1-1-1222211-2-21111-2-2-2-20000000000000000000
χ29444444441-211-2-2-41-21-211-2-211-2-21-211-2-2-4-400033-3-3000033-3-3000033-3-30000-1-122-1-1-1-122220000000000000000000
χ30444444441-211-2-2-41-21-211-2-211-2-21-211-2-2-4-4000-3-3330000-3-3330000-3-3330000-1-122-1-1-1-122220000000000000000000
χ3144444444-21-2-2114-21-21-2-211-2-211-21-2-21144444-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-211-2-2-2-211110000000000000000000
χ3244444444-21-2-2114-21-21-2-211-2-211-21-2-21144-4-4-42222-1-1-1-12222-1-1-1-12222-1-1-1-1-2-211-2-2-2-211110000000000000000000
χ3344444444-21-2-211-4-21-21-2-211-2-211-21-2-211-4-4000000033-3-3000033-3-3000033-3-322-1-12222-1-1-1-10000000000000000000
χ3444444444-21-2-211-4-21-21-2-211-2-211-21-2-211-4-40000000-3-3330000-3-3330000-3-33322-1-12222-1-1-1-10000000000000000000
χ354444-2-2-2-21-2−1−3i32−1+3i321141-21-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i3211-2-24-2-21111-2-2-2-2−1−3i32−1−3i32−1+3i32−1+3i321111−1+3i32−1+3i32−1−3i32−1−3i32111111-2-2−1−3i32−1−3i32−1+3i32−1+3i3211110000000000000000000
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χ374444-2-2-2-21-2−1−3i32−1+3i3211-41-21-2−1−3i32−1+3i3211−1−3i32−1+3i32111-2−1−3i32−1+3i3211220−2i32i333-3-30000−3−i32−3−i323−i323−i32i3i3i3i3−3+i32−3+i323+i323+i32−i3−i3−i3−i3-1-1221+3i321+3i321−3i321−3i32-1-1-1-10000000000000000000
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χ404444-2-2-2-21-2−1+3i32−1−3i321141-21-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i3211-2-2-422-1-1-1-122221−3i321−3i321+3i321+3i32-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-111-2-2−1+3i32−1+3i32−1−3i32−1−3i3211110000000000000000000
χ414444-2-2-2-21-2−1+3i32−1−3i3211-41-21-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i3211220−2i32i3-3-33300003−i323−i32−3−i32−3−i32i3i3i3i33+i323+i32−3+i32−3+i32−i3−i3−i3−i3-1-1221−3i321−3i321+3i321+3i32-1-1-1-10000000000000000000
χ424444-2-2-2-21-2−1+3i32−1−3i3211-41-21-2−1+3i32−1−3i3211−1+3i32−1−3i32111-2−1+3i32−1−3i32112202i3−2i333-3-30000−3+i32−3+i323+i323+i32−i3−i3−i3−i3−3−i32−3−i323−i323−i32i3i3i3i3-1-1221−3i321−3i321+3i321+3i32-1-1-1-10000000000000000000
χ434444-2-2-2-2-2111−1−3i32−1+3i324-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-24-2-2-2-2-2-211111111−1−3i32−1−3i32−1+3i32−1+3i321111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i320000000000000000000
χ444444-2-2-2-2-2111−1−3i32−1+3i324-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-2-4222222-1-1-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-11−3i321−3i321+3i321+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i320000000000000000000
χ454444-2-2-2-2-2111−1−3i32−1+3i32-4-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2111−1−3i32−1+3i32220−2i32i3000033-3-3i3i3i3i3−3−i32−3−i323−i323−i32−i3−i3−i3−i3−3+i32−3+i323+i323+i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i320000000000000000000
χ464444-2-2-2-2-2111−1−3i32−1+3i32-4-21-2111−1−3i32−1+3i3211−1−3i32−1+3i32-2111−1−3i32−1+3i322202i3−2i30000-3-333−i3−i3−i3−i33+i323+i32−3+i32−3+i32i3i3i3i33−i323−i32−3−i32−3−i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i320000000000000000000
χ474444-2-2-2-2-2111−1+3i32−1−3i324-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-24-2-2-2-2-2-211111111−1+3i32−1+3i32−1−3i32−1−3i321111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i320000000000000000000
χ484444-2-2-2-2-2111−1+3i32−1−3i324-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-2-4222222-1-1-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-11+3i321+3i321−3i321−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i320000000000000000000
χ494444-2-2-2-2-2111−1+3i32−1−3i32-4-21-2111−1+3i32−1−3i3211−1+3i32−1−3i32-2111−1+3i32−1−3i32220−2i32i30000-3-333i3i3i3i33−i323−i32−3−i32−3−i32−i3−i3−i3−i33+i323+i32−3+i32−3+i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i320000000000000000000
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χ5144-4-4-2-22244-2-2-2-2044-4-4-2-2-2-22222-4-4222200000000000000000000000000000000000000000004i−4i00−2i2i00000000000
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χ554-4-444-4-441-211-2-20-12-12-1-122-1-1221-211-2-200000−i3i3−i3i300−2i32i3−i3i3−i3i300−2i32i3−i3i3−i3i300−2i32i33-3003-33-300000000000000000000000
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χ694-4-44-222-21-2−1+3i32−1−3i32110-12-121−3i321+3i32-1-11−3i321+3i32-1-11-2−1+3i32−1−3i3211−2i32i3000i3−i3−i3i32i3−2i3003−i32−3+i323+i32−3−i32−i3i33-3−3−i323+i32−3+i323−i32−i3i3-33-33003−i32−3+i323+i32−3−i32−i3i3i3−i30000000000000000000
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χ724-4-44-222-244-2-2-2-20-4-4-4-42222222244-2-2-2-2−2i32i30000000000000000000000000000000−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000
χ734-4-44-222-244-2-2-2-20-4-4-4-42222222244-2-2-2-22i3−2i300000000000000000000000000000002i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000
χ744-4-44-222-2-2111−1−3i32−1+3i3202-12-1-1-11+3i321−3i32-1-11+3i321−3i32-2111−1−3i32−1+3i32−2i32i3000−2i32i300i3−i3i3−i3i3−i3-33−3−i323+i323−i32−3+i32i3−i33-33−i32−3+i32−3−i323+i3200-33i3−i3−i3i33+i32−3−i323−i32−3+i320000000000000000000
χ754-4-44-222-2-2111−1−3i32−1+3i3202-12-1-1-11+3i321−3i32-1-11+3i321−3i32-2111−1−3i32−1+3i32−2i32i30002i3−2i300−i3i3−i3i3−i3i33-33+i32−3−i32−3+i323−i32−i3i3-33−3+i323−i323+i32−3−i3200-33i3−i3−i3i33+i32−3−i323−i32−3+i320000000000000000000
χ764-4-44-222-2-2111−1−3i32−1+3i3202-12-1-1-11+3i321−3i32-1-11+3i321−3i32-2111−1−3i32−1+3i322i3−2i300000−2i32i3−i3i3i3−i3-33i3−i33+i32−3−i323−i32−3+i323-3i3−i3−3+i323−i32−3−i323+i32003-3−i3i3i3−i3−3−i323+i32−3+i323−i320000000000000000000
χ774-4-44-222-2-2111−1−3i32−1+3i3202-12-1-1-11+3i321−3i32-1-11+3i321−3i32-2111−1−3i32−1+3i322i3−2i3000002i3−2i3i3−i3−i3i33-3−i3i3−3−i323+i32−3+i323−i32-33−i3i33−i32−3+i323+i32−3−i32003-3−i3i3i3−i3−3−i323+i32−3+i323−i320000000000000000000
χ784-4-44-222-2-2111−1+3i32−1−3i3202-12-1-1-11−3i321+3i32-1-11−3i321+3i32-2111−1+3i32−1−3i32−2i32i300000−2i32i3−i3i3i3−i33-3i3−i3−3+i323−i32−3−i323+i32-33i3−i33+i32−3−i323−i32−3+i32003-3i3−i3−i3i3−3+i323−i32−3−i323+i320000000000000000000
χ794-4-44-222-2-2111−1+3i32−1−3i3202-12-1-1-11−3i321+3i32-1-11−3i321+3i32-2111−1+3i32−1−3i32−2i32i3000002i3−2i3i3−i3−i3i3-33−i3i33−i32−3+i323+i32−3−i323-3−i3i3−3−i323+i32−3+i323−i32003-3i3−i3−i3i3−3+i323−i32−3−i323+i320000000000000000000
χ804-4-44-222-2-2111−1+3i32−1−3i3202-12-1-1-11−3i321+3i32-1-11−3i321+3i32-2111−1+3i32−1−3i322i3−2i3000−2i32i300i3−i3i3−i3i3−i33-33−i32−3+i32−3−i323+i32i3−i3-33−3−i323+i323−i32−3+i3200-33−i3i3i3−i33−i32−3+i323+i32−3−i320000000000000000000
χ814-4-44-222-2-2111−1+3i32−1−3i3202-12-1-1-11−3i321+3i32-1-11−3i321+3i32-2111−1+3i32−1−3i322i3−2i30002i3−2i300−i3i3−i3i3−i3i3-33−3+i323−i323+i32−3−i32−i3i33-33+i32−3−i32−3+i323−i3200-33−i3i3i3−i33−i32−3+i323+i32−3−i320000000000000000000
χ8288-8-888-8-82-422-4-402-4-2422-4-4-2-244-24-2-244000000000000000000000000000000000000000000000000000000000000
χ8388-8-888-8-8-42-4-4220-424-2-4-42244-2-24-244-2-2000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-4-4442-4−1−3i3−1+3i32202-4-24−1−3i3−1+3i3221+3i31−3i3-2-2-241+3i31−3i3-2-2000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-4-4442-4−1+3i3−1−3i32202-4-24−1+3i3−1−3i3221−3i31+3i3-2-2-241−3i31+3i3-2-2000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-4-444-4222−1−3i3−1+3i30-424-222−1−3i3−1+3i3-2-21+3i31−3i34-2-2-21+3i31−3i3000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-4-444-4222−1+3i3−1−3i30-424-222−1+3i3−1−3i3-2-21−3i31+3i34-2-2-21−3i31+3i3000000000000000000000000000000000000000000000000000000000000
χ888-88-88-88-82-422-4-40-242-4-2-24422-4-4-24-2-244000000000000000000000000000000000000000000000000000000000000
χ898-88-88-88-8-42-4-42204-2-4244-2-2-4-4224-244-2-2000000000000000000000000000000000000000000000000000000000000
χ908-88-8-44-442-4−1−3i3−1+3i3220-242-41+3i31−3i3-2-2−1−3i3−1+3i322-241+3i31−3i3-2-2000000000000000000000000000000000000000000000000000000000000
χ918-88-8-44-442-4−1+3i3−1−3i3220-242-41−3i31+3i3-2-2−1+3i3−1−3i322-241−3i31+3i3-2-2000000000000000000000000000000000000000000000000000000000000
χ928-88-8-44-44-4222−1−3i3−1+3i304-2-42-2-21+3i31−3i322−1−3i3−1+3i34-2-2-21+3i31−3i3000000000000000000000000000000000000000000000000000000000000
χ938-88-8-44-44-4222−1+3i3−1−3i304-2-42-2-21−3i31+3i322−1+3i3−1−3i34-2-2-21−3i31+3i3000000000000000000000000000000000000000000000000000000000000

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