Finite Group Databasebeta

← Group #13181172

Character table — Group #13181172

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222224444888888888899181818181818181818181818181818181836363636727272721122222444488888888889918181818181818181818181818181818183636363672727272
order12236663366336666666622244446666121212121212121222446612122226666666666666666662224444666612121212121212122244661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-11
χ511-111-1-1111111-1-111-1-1-1-111-111-1-11-1-111111-1-1-1-111-1-111-1-111-111-1-1111111-1-111-1-1-1-111-111-1-11-1-111111-1-1-1-111-1-111-1-1
χ611-111-1-1111111-1-111-1-1-1-111-111-1-11-1-111111-1-1-1-1-1-111-1-11111-111-1-1111111-1-111-1-1-1-111-111-1-11-1-111111-1-1-1-1-1-111-1-111
χ711-111-1-1111111-1-111-1-1-1-111-1-1-1111-1-11-1-1-1-111111-1-111-1-1111-111-1-1111111-1-111-1-1-1-111-1-1-1111-1-11-1-1-1-111111-1-111-1-11
χ811-111-1-1111111-1-111-1-1-1-111-1-1-1111-1-11-1-1-1-11111-111-1-111-111-111-1-1111111-1-111-1-1-1-111-1-1-1111-1-11-1-1-1-11111-111-1-111-1
χ9222222222222222222222-2-2-20000-2-2-2-20000000000000000222222222222222222222-2-2-20000-2-2-2-20000000000000000
χ10222-1-1-1-12222-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-100000000222-1-1-1-12222-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ11222-1-1-1-12222-1-122-1-1-1-1-1-1222-2-2-2-2-1-1-1-11111111100000000222-1-1-1-12222-1-122-1-1-1-1-1-1222-2-2-2-2-1-1-1-11111111100000000
χ12222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-20000111133−3−333−3−300000000222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-20000111133−3−333−3−300000000
χ13222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-200001111−3−333−3−33300000000222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-200001111−3−333−3−33300000000
χ1422-222-2-2222222-2-222-2-2-2-2-2-220000-222-2000000000000000022-222-2-2222222-2-222-2-2-2-2-2-220000-222-20000000000000000
χ1522-2-1-1112222-1-1-2-2-1-1111122-222-2-2-111-1-1-1-1-111110000000022-2-1-1112222-1-1-2-2-1-1111122-222-2-2-111-1-1-1-1-1111100000000
χ1622-2-1-1112222-1-1-2-2-1-1111122-2-2-222-111-11111-1-1-1-10000000022-2-1-1112222-1-1-2-2-1-1111122-2-2-222-111-11111-1-1-1-100000000
χ1722-2-1-1112222-1-1-2-2-1-11111-2-2200001-1-1133−3−3−3−3330000000022-2-1-1112222-1-1-2-2-1-11111-2-2200001-1-1133−3−3−3−33300000000
χ1822-2-1-1112222-1-1-2-2-1-11111-2-2200001-1-11−3−33333−3−30000000022-2-1-1112222-1-1-2-2-1-11111-2-2200001-1-11−3−33333−3−300000000
χ192-202-20022-2-22200-2-200002-20002i−2i200-200002i−2i2i−2i000000002-202-20022-2-22200-2-200002-20002i−2i200-200002i−2i2i−2i00000000
χ202-202-20022-2-22200-2-200002-2000−2i2i200-20000−2i2i−2i2i000000002-202-20022-2-22200-2-200002-2000−2i2i200-20000−2i2i−2i2i00000000
χ212-202-20022-2-22200-2-20000-2202-200-20022-22-20000000000002-202-20022-2-22200-2-20000-2202-200-20022-22-2000000000000
χ222-202-20022-2-22200-2-20000-220-2200-2002-22-220000000000002-202-20022-2-22200-2-20000-220-2200-2002-22-22000000000000
χ232-20-11−i3i322-2-2-1-10011−i3−i3i3i32-20002i−2i-1−i3i313−3−33−ii−ii000000002-20-11−i3i322-2-2-1-10011−i3−i3i3i32-20002i−2i-1−i3i313−3−33−ii−ii00000000
χ242-20-11−i3i322-2-2-1-10011−i3−i3i3i32-2000−2i2i-1−i3i31−333−3i−ii−i000000002-20-11−i3i322-2-2-1-10011−i3−i3i3i32-2000−2i2i-1−i3i31−333−3i−ii−i00000000
χ252-20-11−i3i322-2-2-1-10011−i3−i3i3i3-2202-2001i3−i3-1-11-11−i3i3i3−i3000000002-20-11−i3i322-2-2-1-10011−i3−i3i3i3-2202-2001i3−i3-1-11-11−i3i3i3−i300000000
χ262-20-11−i3i322-2-2-1-10011−i3−i3i3i3-220-22001i3−i3-11-11-1i3−i3−i3i3000000002-20-11−i3i322-2-2-1-10011−i3−i3i3i3-220-22001i3−i3-11-11-1i3−i3−i3i300000000
χ272-20-11i3−i322-2-2-1-10011i3i3−i3−i32-20002i−2i-1i3−i31−333−3−ii−ii000000002-20-11i3−i322-2-2-1-10011i3i3−i3−i32-20002i−2i-1i3−i31−333−3−ii−ii00000000
χ282-20-11i3−i322-2-2-1-10011i3i3−i3−i32-2000−2i2i-1i3−i313−3−33i−ii−i000000002-20-11i3−i322-2-2-1-10011i3i3−i3−i32-2000−2i2i-1i3−i313−3−33i−ii−i00000000
χ292-20-11i3−i322-2-2-1-10011i3i3−i3−i3-2202-2001−i3i3-1-11-11i3−i3−i3i3000000002-20-11i3−i322-2-2-1-10011i3i3−i3−i3-2202-2001−i3i3-1-11-11i3−i3−i3i300000000
χ302-20-11i3−i322-2-2-1-10011i3i3−i3−i3-220-22001−i3i3-11-11-1−i3i3i3−i3000000002-20-11i3−i322-2-2-1-10011i3i3−i3−i3-220-22001−i3i3-11-11-1−i3i3i3−i300000000
χ3144444441-21-21-21-21-21-21-2000000000000000000002020-10-144444441-21-21-21-21-21-21-2000000000000000000002020-10-1
χ3244444441-21-21-21-21-21-21-200000000000000000000-20-2010144444441-21-21-21-21-21-21-200000000000000000000-20-20101
χ334444444-21-21-21-21-21-21-2100000000000000000002020-10-104444444-21-21-21-21-21-21-2100000000000000000002020-10-10
χ344444444-21-21-21-21-21-21-210000000000000000000-20-2010104444444-21-21-21-21-21-21-210000000000000000000-20-201010
χ3544-444-4-41-21-21-2-121-2-12-120000000000000000000020-20-10144-444-4-41-21-21-2-121-2-12-120000000000000000000020-20-101
χ3644-444-4-41-21-21-2-121-2-12-1200000000000000000000-202010-144-444-4-41-21-21-2-121-2-12-1200000000000000000000-202010-1
χ3744-444-4-4-21-21-212-1-212-12-1000000000000000000020-20-101044-444-4-4-21-21-212-1-212-12-1000000000000000000020-20-1010
χ3844-444-4-4-21-21-212-1-212-12-10000000000000000000-202010-1044-444-4-4-21-21-212-1-212-12-10000000000000000000-202010-10
χ39888-4-4-4-42-42-4-122-4-12-12-12000000000000000000000000000888-4-4-4-42-42-4-122-4-12-12-12000000000000000000000000000
χ40888-4-4-4-4-42-422-1-422-12-12-1000000000000000000000000000888-4-4-4-4-42-422-1-422-12-12-1000000000000000000000000000
χ4188-8-4-4442-42-4-12-24-121-21-200000000000000000000000000088-8-4-4442-42-4-12-24-121-21-2000000000000000000000000000
χ4288-8-4-444-42-422-14-22-1-21-2100000000000000000000000000088-8-4-444-42-422-14-22-1-21-21000000000000000000000000000
χ438-808-8002-4-242-400-2400000000000000000000000000000008-808-8002-4-242-400-240000000000000000000000000000000
χ448-808-800-424-2-42004-200000000000000000000000000000008-808-800-424-2-42004-20000000000000000000000000000000
χ458-80-44−4i34i32-4-24-12001-2−i32i3i3−2i30000000000000000000000000008-80-44−4i34i32-4-24-12001-2−i32i3i3−2i3000000000000000000000000000
χ468-80-44−4i34i3-424-22-100-212i3−i3−2i3i30000000000000000000000000008-80-44−4i34i3-424-22-100-212i3−i3−2i3i3000000000000000000000000000
χ478-80-444i3−4i32-4-24-12001-2i3−2i3−i32i30000000000000000000000000008-80-444i3−4i32-4-24-12001-2i3−2i3−i32i3000000000000000000000000000
χ488-80-444i3−4i3-424-22-100-21−2i3i32i3−i30000000000000000000000000008-80-444i3−4i3-424-22-100-21−2i3i32i3−i3000000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ501111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-11-11-11
χ52111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-11-11-1
χ5311-111-1-1111111-1-111-1-1-1-111-111-1-11-1-111111-1-1-1-111-1-111-1-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-11-1-111-111-1-1-1-1-11111-1-111-1-111
χ5411-111-1-1111111-1-111-1-1-1-111-111-1-11-1-111111-1-1-1-1-1-111-1-111-1-11-1-111-1-1-1-1-1-111-1-11111-1-11-1-111-111-1-1-1-1-1111111-1-111-1-1
χ5511-111-1-1111111-1-111-1-1-1-111-1-1-1111-1-11-1-1-1-111111-1-111-1-11-1-11-1-111-1-1-1-1-1-111-1-11111-1-1111-1-1-111-11111-1-1-1-1-111-1-111-1
χ5611-111-1-1111111-1-111-1-1-1-111-1-1-1111-1-11-1-1-1-11111-111-1-111-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-1111-1-1-111-11111-1-1-1-11-1-111-1-11
χ57222222222222222222222-2-2-20000-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222000022220000000000000000
χ58222-1-1-1-12222-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-21111-2-2-2-211-2-2111111-2-2-2-2-2-2-211111111111100000000
χ59222-1-1-1-12222-1-122-1-1-1-1-1-1222-2-2-2-2-1-1-1-11111111100000000-2-2-21111-2-2-2-211-2-2111111-2-2-222221111-1-1-1-1-1-1-1-100000000
χ60222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-20000111133−3−333−3−300000000-2-2-21111-2-2-2-211-2-21111112220000-1-1-1-1−3−333−3−33300000000
χ61222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-200001111−3−333−3−33300000000-2-2-21111-2-2-2-211-2-21111112220000-1-1-1-133−3−333−3−300000000
χ6222-222-2-2222222-2-222-2-2-2-2-2-220000-222-20000000000000000-2-22-2-222-2-2-2-2-2-222-2-2222222-200002-2-220000000000000000
χ6322-2-1-1112222-1-1-2-2-1-1111122-222-2-2-111-1-1-1-1-1111100000000-2-2211-1-1-2-2-2-2112211-1-1-1-1-2-22-2-2221-1-111111-1-1-1-100000000
χ6422-2-1-1112222-1-1-2-2-1-1111122-2-2-222-111-11111-1-1-1-100000000-2-2211-1-1-2-2-2-2112211-1-1-1-1-2-2222-2-21-1-11-1-1-1-1111100000000
χ6522-2-1-1112222-1-1-2-2-1-11111-2-2200001-1-1133−3−3−3−33300000000-2-2211-1-1-2-2-2-2112211-1-1-1-122-20000-111-1−3−33333−3−300000000
χ6622-2-1-1112222-1-1-2-2-1-11111-2-2200001-1-11−3−33333−3−300000000-2-2211-1-1-2-2-2-2112211-1-1-1-122-20000-111-133−3−3−3−33300000000
χ672-202-20022-2-22200-2-200002-20002i−2i200-200002i−2i2i−2i00000000-220-2200-2-222-2-200220000-22000−2i2i-20020000−2i2i−2i2i00000000
χ682-202-20022-2-22200-2-200002-2000−2i2i200-20000−2i2i−2i2i00000000-220-2200-2-222-2-200220000-220002i−2i-200200002i−2i2i−2i00000000
χ692-202-20022-2-22200-2-20000-2202-200-20022-22-2000000000000-220-2200-2-222-2-2002200002-20-2200200-2-22-22000000000000
χ702-202-20022-2-22200-2-20000-220-2200-2002-22-22000000000000-220-2200-2-222-2-2002200002-202-200200-22-22-2000000000000
χ712-20-11−i3i322-2-2-1-10011−i3−i3i3i32-20002i−2i-1−i3i313−3−33−ii−ii00000000-2201-1i3−i3-2-2221100-1-1i3i3−i3−i3-22000−2i2i1i3−i3-1−333−3i−ii−i00000000
χ722-20-11−i3i322-2-2-1-10011−i3−i3i3i32-2000−2i2i-1−i3i31−333−3i−ii−i00000000-2201-1i3−i3-2-2221100-1-1i3i3−i3−i3-220002i−2i1i3−i3-13−3−33−ii−ii00000000
χ732-20-11−i3i322-2-2-1-10011−i3−i3i3i3-2202-2001i3−i3-1-11-11−i3i3i3−i300000000-2201-1i3−i3-2-2221100-1-1i3i3−i3−i32-20-2200-1−i3i311-11-1i3−i3−i3i300000000
χ742-20-11−i3i322-2-2-1-10011−i3−i3i3i3-220-22001i3−i3-11-11-1i3−i3−i3i300000000-2201-1i3−i3-2-2221100-1-1i3i3−i3−i32-202-200-1−i3i31-11-11−i3i3i3−i300000000
χ752-20-11i3−i322-2-2-1-10011i3i3−i3−i32-20002i−2i-1i3−i31−333−3−ii−ii00000000-2201-1−i3i3-2-2221100-1-1−i3−i3i3i3-22000−2i2i1−i3i3-13−3−33i−ii−i00000000
χ762-20-11i3−i322-2-2-1-10011i3i3−i3−i32-2000−2i2i-1i3−i313−3−33i−ii−i00000000-2201-1−i3i3-2-2221100-1-1−i3−i3i3i3-220002i−2i1−i3i3-1−333−3−ii−ii00000000
χ772-20-11i3−i322-2-2-1-10011i3i3−i3−i3-2202-2001−i3i3-1-11-11i3−i3−i3i300000000-2201-1−i3i3-2-2221100-1-1−i3−i3i3i32-20-2200-1i3−i311-11-1−i3i3i3−i300000000
χ782-20-11i3−i322-2-2-1-10011i3i3−i3−i3-220-22001−i3i3-11-11-1−i3i3i3−i300000000-2201-1−i3i3-2-2221100-1-1−i3−i3i3i32-202-200-1i3−i31-11-11i3−i3−i3i300000000
χ7944444441-21-21-21-21-21-21-2000000000000000000002020-10-1-4-4-4-4-4-4-4-12-12-12-12-12-12-1200000000000000000000-20-20101
χ8044444441-21-21-21-21-21-21-200000000000000000000-20-20101-4-4-4-4-4-4-4-12-12-12-12-12-12-12000000000000000000002020-10-1
χ814444444-21-21-21-21-21-21-2100000000000000000002020-10-10-4-4-4-4-4-4-42-12-12-12-12-12-12-10000000000000000000-20-201010
χ824444444-21-21-21-21-21-21-210000000000000000000-20-201010-4-4-4-4-4-4-42-12-12-12-12-12-12-100000000000000000002020-10-10
χ8344-444-4-41-21-21-2-121-2-12-120000000000000000000020-20-101-4-44-4-444-12-12-121-2-121-21-200000000000000000000-202010-1
χ8444-444-4-41-21-21-2-121-2-12-1200000000000000000000-202010-1-4-44-4-444-12-12-121-2-121-21-20000000000000000000020-20-101
χ8544-444-4-4-21-21-212-1-212-12-1000000000000000000020-20-1010-4-44-4-4442-12-12-1-212-1-21-210000000000000000000-202010-10
χ8644-444-4-4-21-21-212-1-212-12-10000000000000000000-202010-10-4-44-4-4442-12-12-1-212-1-21-21000000000000000000020-20-1010
χ87888-4-4-4-42-42-4-122-4-12-12-12000000000000000000000000000-8-8-84444-24-241-2-241-21-21-2000000000000000000000000000
χ88888-4-4-4-4-42-422-1-422-12-12-1000000000000000000000000000-8-8-844444-24-2-214-2-21-21-21000000000000000000000000000
χ8988-8-4-4442-42-4-12-24-121-21-2000000000000000000000000000-8-8844-4-4-24-241-22-41-2-12-12000000000000000000000000000
χ9088-8-4-444-42-422-14-22-1-21-21000000000000000000000000000-8-8844-4-44-24-2-21-42-212-12-1000000000000000000000000000
χ918-808-8002-4-242-400-240000000000000000000000000000000-880-8800-242-4-24002-40000000000000000000000000000000
χ928-808-800-424-2-42004-20000000000000000000000000000000-880-88004-2-424-200-420000000000000000000000000000000
χ938-80-44−4i34i32-4-24-12001-2−i32i3i3−2i3000000000000000000000000000-8804-44i3−4i3-242-41-200-12i3−2i3−i32i3000000000000000000000000000
χ948-80-44−4i34i3-424-22-100-212i3−i3−2i3i3000000000000000000000000000-8804-44i3−4i34-2-42-21002-1−2i3i32i3−i3000000000000000000000000000
χ958-80-444i3−4i32-4-24-12001-2i3−2i3−i32i3000000000000000000000000000-8804-4−4i34i3-242-41-200-12−i32i3i3−2i3000000000000000000000000000
χ968-80-444i3−4i3-424-22-100-21−2i3i32i3−i3000000000000000000000000000-8804-4−4i34i34-2-42-21002-12i3−i3−2i3i3000000000000000000000000000

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