Finite Group Databasebeta

← Group #13168736

Character table — Group #13168736

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212444466661212121212121212121212122244444412121212661212121212121212121212121212446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-11111111111-1-111-1-11111-1-1-1-1111111-11-111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111111111-1111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111-11111-1-111-1-1111-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-1-1-1-11-1-111-1-11-111
χ51111111111111111111111111111111-1-111111111111111111111-11-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-111111111-11-1-111-1-11-1-1-1
χ61111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-11-1-1-1-1-111-1111
χ71111111111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-11-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-111-1-1-1-1111-11111-1-1-11-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-11-1-1-11111-1-1-1-1-1111-1-1111-11-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1111111111111-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-11-1-111111-1-1-1-111-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-111-1111-1-1-1-11111-1111-1-1111-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-111111-1-11111-1-11-11111-1-1-111-1
χ17222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1202022-1-1-1-122-1-100-1-10022220000-1-1-1-1-1-10202-1-1-1-100-1-10000-1-100000000
χ18222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-1-202022-1-1-1-1-2-211001100-2-2-2-200001111-1-10-202-1-111001100001100000000
χ19222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-120-20-2-2111122-1-100-1-100-2-2-2-20000111111020-211-1-100-1-100001100000000
χ20222222-122-1-122-1222-1-122-1-1-12-1-12-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-1-20-20-2-21111-2-21100110022220000-1-1-1-1110-20-2111100110000-1-100000000
χ21222222-122-1-122-1222-1-1-22-1-1-12-1-12-1112222-1-1-1-1-2-211-2-2111111-20-2022-1-11122-1-100110022-2-200001111-1-10-20-211-1-100110000-1-100000000
χ22222222-122-1-122-1222-1-1-22-1-1-12-1-12-11122-2-2-1-1-1-1-2-211-2-211111120-2022-1-111-2-21100-1-100-2-2220000-1-1-1-1-1-1020-2111100-1-100001100000000
χ23222222-122-1-122-1222-1-1-22-1-1-12-1-12-111-2-222-1-1-1-1-2-211-2-2111111-2020-2-211-1-122-1-1001100-2-2220000-1-1-1-1110-202-1-1-1-1001100001100000000
χ24222222-122-1-122-1222-1-1-22-1-1-12-1-12-111-2-2-2-2-1-1-1-1-2-211-2-21111112020-2-211-1-1-2-21100-1-10022-2-200001111110202-1-11100-1-10000-1-100000000
χ2522222-12-1222-1222-1-12-12-12-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-10222-1-1222200002200-1-1000022000000-1-1-102-1-1-100-1-100-1-1200000-1-10-100
χ2622222-12-1222-1222-1-12-12-12-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-10-22-2-1-122220000-2-200110000-2-2000000-1-110-2-1-1-100110011-200000110100
χ2722222-12-1222-1222-1-12-12-12-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-102-2211-2-2-2-200002200-1-10000-2-200000011-10211100-1-100-1-1-200000110100
χ2822222-12-1222-1222-1-12-12-12-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-10-2-2-211-2-2-2-20000-2-200110000220000001110-211100110011200000-1-10-100
χ2922222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-11-21111-2-2111102-2-2-1-122-2-200002200110000-2-2000000-1-1-10-2111001100-1-1200000110-100
χ3022222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-22200-1-1-1-11-21111-2-211110-2-22-1-122-2-20000-2-200-1-1000022000000-1-110211100-1-10011-200000-1-10100
χ3122222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-21111022-211-2-222000022001100002200000011-10-2-1-1-1001100-1-1-200000-1-10100
χ3222222-12-1222-1222-1-12-1-2-12-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-211110-22211-2-2220000-2-200-1-10000-2-200000011102-1-1-100-1-10011200000110-100
χ332222-1222-1222-12-12-1-122-1-122-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12202000000-1-122-1-12222000000220000002-1-1000-1-1-1-1-1-1-1-10200-1-100-1000
χ342222-1222-1222-12-12-1-122-1-122-1-12-1-1220022-1-1-1-12-122-1-1-1-1-1-1-1-12-20-2000000-1-1221122-2-2000000-2-2000000-2-11000-1-111-1-1110-20011001000
χ352222-1222-1222-12-12-1-122-1-122-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-220200000011-2-2-1-1-2-222000000-2-200000021-100011-1-111-1-10-20011001000
χ362222-1222-1222-12-12-1-122-1-122-1-12-1-12200-2-2-1-1-1-12-122-1-1-1-1-1-1-1-1-2-20-200000011-2-211-2-2-2-200000022000000-211000111111110200-1-100-1000
χ372222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-1-21-2-211111111-220-2000000-1-122-1-1-2-2-2-200000022000000211000-1-11111-1-10-200-1-1001000
χ382222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-20022-1-1-1-1-21-2-211111111-2-202000000-1-12211-2-222000000-2-2000000-21-1000-1-1-1-1111102001100-1000
χ392222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-1-21-2-211111111220-200000011-2-2-1-122-2-2000000-2-20000002-110001111-1-1-1-102001100-1000
χ402222-1222-1222-12-12-1-12-2-1-122-1-12-1-1-2-200-2-2-1-1-1-1-21-2-2111111112-20200000011-2-211222200000022000000-2-1-100011-1-1-1-1110-200-1-1001000
χ4122-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-2002-22-222-2-200000000000000002-22-2002-22-20000002-200000000002-20000002-2000000002-200000000
χ4222-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-2002-2-2222-2-200000000000000002-22-200-22-22000000-2200000000002-2000000-2200000000-2200000000
χ4322-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-200-222-222-2-20000000000000000-22-22002-22-2000000-220000000000-220000002-200000000-2200000000
χ4422-2-2222222-2-2-2-2-2-222202-22-2-22-2-2-200-22-2222-2-20000000000000000-22-2200-22-220000002-20000000000-22000000-22000000002-200000000
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χ4722-2-222-122-11-2-21-2-22-1-1021-11-2-11-213−3-222-2-1-111003−3003−333−3−30000-221-1−332-2-11003−300-22000000−3−3331-10000−33-11003−300001-100000000
χ4822-2-222-122-11-2-21-2-22-1-1021-11-2-11-213−3-22-22-1-111003−3003−333−3−30000-221-1−33-221-100−33002-200000033−3−31-10000−331-100−330000-1100000000
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χ5122-2-222-122-11-2-21-2-22-1-1021-11-2-11-21−33-222-2-1-11100−3300−33−3−3330000-221-13−32-2-1100−3300-2200000033−3−31-100003−3-1100−3300001-100000000
χ5222-2-222-122-11-2-21-2-22-1-1021-11-2-11-21−33-22-22-1-11100−3300−33−3−3330000-221-13−3-221-1003−3002-2000000−3−3331-100003−31-1003−30000-1100000000
χ532-22-2222-2-2-2-2222-2-22220-2-2-22-2-2-2220000002-2-2200000000000000000000000000000000002-22i−2i2i−2i2-22-2000000000000000000002i−2i2i−2i0000
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χ944-4-44-2-2422-4422-4-2-21-2-20-1-22212-2-120000001-11-100003i−3i003i−3i3i−3i0000000000000023−2300−2i32i30000000000000000000000i3−i300−33000000000000
χ954-4-44-2-2422-4422-4-2-21-2-20-1-22212-2-120000001-11-100003i−3i003i−3i3i−3i00000000000000−2323002i3−2i30000000000000000000000−i3i3003−3000000000000
χ964-4-44-2-2422-4422-4-2-21-2-20-1-22212-2-120000001-11-10000−3i3i00−3i3i−3i3i0000000000000023−23002i3−2i30000000000000000000000−i3i300−33000000000000
χ974-4-44-2-2422-4422-4-2-21-2-20-1-22212-2-120000001-11-10000−3i3i00−3i3i−3i3i00000000000000−232300−2i32i30000000000000000000000i3−i3003−3000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-48-4-48-844-8442-4-4024-44-2-44-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-4-4-444444422202-22-2-22-2-2-243−430000-1-11100−232300−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-4-4-444444422202-22-2-22-2-2-2−43430000-1-1110023−230023−23−3−333000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-44-844-48-4-84-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-4-84448-4-44-8-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4844-8-8-4-48442-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-44444-4-4-4442220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-44444-4-4-4442220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-44-84-44-848-4-4-4204-4-2-2-442440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-48-4-844-4-844-48-42-404244-4-2-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4444-4444-4-42220-22-2-22-22-2-2000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4444-4444-4-42220-22-2-22-22-2-2000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000

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