Finite Group Databasebeta

← Group #13172867

Character table — Group #13172867

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444666666888888888888888899991212121212121212121212121212121212121218181818181818182424242424242424242424242424242436363636363636363654547272108
order12223336666666662333666666666662244443666666666666666444424466666612121212121212121212444412121212666661212121212121212121212244121212121212446122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11111111111111111-1-1-1-111-111111111-1-111-1-1-1-111-1-1-1-1-1-1111111-111111-1-1-1-1-11-111-1-1-1-1-1-1-11-1
χ3111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-111-1-11111-1-111-1-11111-1-111-1-1-1-1-111-1-111111-1-111111-1-1-1-111-1-1-1-11-1-1
χ4111111111111111111111111111111111-1-1-1-111111111111111111111-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11-1111-1-1-1-1-1-1-1-11-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-11111111111111111111111111-1111-1-1-1-11111111111-1-1-1-111111-1-111-11-1-1-1111111-1-11-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-11-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1-1-111-1-1-1-11-1-1-1-111-1-1111-11
χ71111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-11-111-1-1-1-111-111
χ81111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1
χ91111111111111111-1111-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111111111-1-111111111-111-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-1-1
χ101111111111111111-1111-1-11111111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1-11111-1-1-1-1-1-1-111-1-1-11-1-1-111-1-1111-1111-1-111-1-11-11
χ111111111111111111-1111-1-111111111111-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1111111-1-111-1-111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-111
χ121111111111111111-1111-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-111111-11111111-1-1-1-1-1-1-1-111-1-1-1-1111111111-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1
χ131111111111111111-1111-1-1111111111-1-111111-1-1-1-1-1-1-1-1111-1-1-1-11111-11-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-11-11111111-1-111-1-1-1-1-1-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-11111111-1-111-111-1-1111111-11-1
χ151111111111111111-1111-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1111-1111-1-111-1-11-1111-1-111111-1-1
χ161111111111111111-1111-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11111111-1-1-1-111-1-1-11111-1-1-1-1-1-11
χ17222222-12-122-122-122-12-122-122-1-1-1-12-1220022-12-1-1-122-1-1-1-1-1-1-1-1-100000220022-1-1002200-1-122002200000-1-100-1-12-1-100-1-1-1-120000-1-10000-100
χ18222222-12-122-122-122-12-122-122-1-1-1-12-12200-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1000002-20022-1-100-2-20011-2-200-2-200000-1-100-112-1-1001111-20000110000100
χ19222222-12-122-122-122-12-122-122-1-1-1-12-1-2-20022-12-1-1-122-1-1-1-1-1-1-1-1-100000-2200-2-211002200-1-12200-2-20000011001-1-21100-1-1-1-1-20000110000100
χ20222222-12-122-122-122-12-122-122-1-1-1-12-1-2-200-2-2-12-1-1-122-1-1-1-1-1-1-1-1-100000-2-200-2-21100-2-20011-2-2002200000110011-21100111120000-1-10000-100
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χ2522222-12-12222-1-12222-1-1222-1-1-1-122-1-1222200-1-1222-1-1-1-1-1-1-1-1-1-1-1000022022-1-1222200-1-1000022000000-1-1-1-1-120-1-1-1-1-10000020-1-10000000-10
χ2622222-12-12222-1-12222-1-1222-1-1-1-122-1-122-2-200-1-1222-1-1-1-1-1-1-1-1-1-1-10000-220-2-2-1-122-2-200110000-2-20000001-1-11120-1-1-11100000-2011000000010
χ2722222-12-12222-1-12222-1-1222-1-1-1-122-1-1-2-22200-1-1222-1-1-1-1-1-1-1-1-1-1-100002-202211-2-22200-1-10000-2-2000000-111-1-1-20111-1-100000-2011000000010
χ2822222-12-12222-1-12222-1-1222-1-1-1-122-1-1-2-2-2-200-1-1222-1-1-1-1-1-1-1-1-1-1-10000-2-20-2-211-2-2-2-2001100002200000011111-20111110000020-1-10000000-10
χ2922222-12-12222-1-122-22-1-1-2-22-1-1-1-122-1-1222200-11-2-2-21111-1-1-111110000-2-20-2-2-1-1222200-1-10000220000001-1-111-20111-1-100000-20-1-1000000010
χ3022222-12-12222-1-122-22-1-1-2-22-1-1-1-122-1-122-2-200-11-2-2-21111-1-1-1111100002-2022-1-122-2-200110000-2-2000000-1-1-1-1-1-20111110000020110000000-10
χ3122222-12-12222-1-122-22-1-1-2-22-1-1-1-122-1-1-2-22200-11-2-2-21111-1-1-111110000-220-2-211-2-22200-1-10000-2-20000001111120-1-1-1-1-10000020110000000-10
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χ342222-12222-1-12222-12-1-12-1-1-1-1-122-1-1-120022-2-2-122-1-1-1-122-1-1-1-1-1-1-1-2-2-2-220-2-1-10000-1-11122-2-21100001111200-1-10-2000-1-1111100-200001100000
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χ362222-12222-1-12222-12-1-12-1-1-1-1-122-1-1-1200-2-2-2-2-122-1-1-1-122-1-1-1-1-1-1-12222-20-21100001111-2-2-2-2110000-1-1-1-1-200110-20001111110020000-1-100000
χ372222-12222-1-12222-1-2-1-1211-1-1-122-1-1-12002222-1-2-21111-2-2-1-1-111112222-20-2110000-1-1-1-12222110000-1-1-1-1-200110-2000-1-1-1-11100-200001100000
χ382222-12222-1-12222-1-2-1-1211-1-1-122-1-1-120022-2-2-1-2-21111-2-2-1-1-11111-2-2-2-2-202110000-1-11122-2-2-1-100001111-2001102000-1-111-1-10020000-1-100000
χ392222-12222-1-12222-1-2-1-1211-1-1-122-1-1-1200-2-222-1-2-21111-2-2-1-1-11111-2-2-2-220-2-1-1000011-1-1-2-2221100001111200-1-10-200011-1-1110020000-1-100000
χ402222-12222-1-12222-1-2-1-1211-1-1-122-1-1-1200-2-2-2-2-1-2-21111-2-2-1-1-111112222202-1-100001111-2-2-2-2-1-10000-1-1-1-1200-1-1020001111-1-100-200001100000
χ4122-2-22222-22-2-2-2-22-2022200-22-22-22-2-2-20000002000000002-2-200002i2i−2i−2i00000000000000000002i−2i2-22i2i−2i−2i00000000000000000002i−2i2-20000000
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χ522-22-2-122-221-1-22-2-210-1-12−i3i3-111-2211-1-200-22−2i2i-100−i3i3−i3i3001-11−i3−i3i3i32i−2i2i−2i000i3−i300001-1i−i-22−2i2i−330000−ii−ii000i3−i3000001-1i−i−3300000003−300000
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χ924-4-4444-2-42-4-4-2-44240-24-2002-44222-2-4-2-440000-20000000022-20000000000000-442-200000000000000000002-2000000000000000000000000000
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χ944-4-444-242-4-4-442-2-4404-2-200-42-222-442-2-440000-20000000022-200000000000002-2-4400000000000000000002-2000000000000000000000000000
χ954-4-444-2-222-4-4-22-2240-2-210022-2-1-12-2214-4000010000003-3-1-113-33-3000000000-22-2200000000000000000001-1000003-300000000000000000000
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χ984-4-444-2-222-4-4-22-2240-2-210022-2-1-12-221-4400001000000-33-1-11-33-330000000002-22-20000000000000000000-11000003-300000000000000000000
χ994-4-44-244-4-4224-44-4-20-2-240022-2-4-42-224000000-20000000022-200004-4-4400000000000000000000000-222-2000000000000000000000000000000
χ1004-4-44-244-4-4224-44-4-20-2-240022-2-4-42-224000000-20000000022-20000-444-4000000000000000000000002-2-22000000000000000000000000000000
χ1018888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222000000-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000
χ1028888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222000000-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000000000
χ10388-8-88-4-4-448-8444-4-80-4-42004-442-2-444-20000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-48-484-444-8-8-4402-4-400-2-44-442-2440000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-48-4-8-44-844840-42-40042-2-44-44-240000002000000002-2-200000000000000000000000000000000000000000000000000000000000000000
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χ10788-8-8-4-4-4-44-44444-44022200-22-22-22-2-2-2000000-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-44-4-884-444-80-4-4200-444-2244-4-2000000200000000-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-44-44-44-44440222−4i34i32-2-2-22-2-22-2000000-1002i3−2i32i3−2i3001-11−i3−i3i3i30000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-44-44-444402224i3−4i32-2-2-22-2-22-2000000-100−2i32i3−2i32i3001-11i3i3−i3−i30000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4-8444-4-884-402-4-400-24-444-224-4000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-484-84484-4-8-40-42-4004-22444-4-2-4000000200000000-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-44444-44-44-4022200-2-22-2-2-22-22000000-10000006-611-1-33-330000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-44444-44-44-4022200-2-22-2-2-22-22000000-1000000-6611-13-33-30000000000000000000000000000000000000000000000000000000000000

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