Finite Group Databasebeta

← Group #13168589

Character table — Group #13168589

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444444444444466888888888888812121212121212121212121212121212121212121212121212181824242424242424242424242424243636363636363654547272727272108
order1222333666666666333466666666612121212121212124436661212121212121212122222466666666661212121212121212121244666666666661212124444412124412121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1111111-1-1-1111-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-111-1
χ311111111111111111111111111111111111111111111111111111-1-1111111-1-111111111111111-1-11-1-1-1111-1-1-1-11111-1-1-11-1-1-1-11-11-1-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-11-1-1-11
χ51111111111111111111111111111111111111-1-11111111111111-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-11-1-1-111-1-1-11-1-1-1-1
χ61111111111111111111111111111111111111-1-11111111111111-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-11-1-1-11-1-1111-11-1-11
χ71111111111111111111111111111111111111-1-11111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1111-1-111-1-1-111-1-1-1111
χ81111111111111111111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-111-1-1-1-111-1-1111111-1-111-1-111111-1-1-1-1-1-111-11-1-1-1-111-11-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111111111-11-1-1-1-1-111-1-11111-11-1-11111-1-111-1-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-111111-1-111-1-1-1-1-1-11111111-1-1-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-11111111-11-1-1-1-1-1-111-111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-111-11-1-1-111-111-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111111111111-1-111-1-1-1-1-1-111-11-1-1-1-1-111-1-1111-1-1-11111-1-11-1-1-111
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-11111-1-11111-1-1-1-1-1-1-1-1-1-1111-111111-1-111-1-1-11-11-1-111-1-1-1-111-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-111-11-1-11111-11-1-1
χ17222222-12-1222-1-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-1022220000-1-1000000-1-100000022222-1-1-1-1-1-1-1-12-1-102000-1-1000-10000
χ18222222-12-1222-1-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-1022-2-20000-1-100000011000000-2-2-222-1111-1-1-1-1-2110-20001100010000
χ19222222-12-1222-1-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-2-222000011000000-1-1000000-2-22-2-21-1-1-111112-1-10-20001100010000
χ20222222-12-1222-1-1222-1-1222-1-1-1-1-1-122222222200-1-1-1-1-1-1-1-1-1-1-1-1-10-2-2-2-20000110000001100000022-2-2-211111111-21102000-1-1000-10000
χ21222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-111111111102-22-20000-1-100000011000000-2-222-21-1-1-1-1-111-2110200011000-10000
χ22222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-111111111102-2-220000-1-1000000-1-100000022-22-21111-1-1112-1-10-2000-1-100010000
χ23222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-11111111110-222-200001100000011000000222-22-1-1-1-111-1-1-2110-2000-1-100010000
χ24222222-12-1222-1-1222-1-1-222-1-1-1-1-1-12-2-2-2-2-2-2-2-200-1-1-1-11111111110-22-22000011000000-1-1000000-2-2-2-22-111111-1-12-1-10200011000-10000
χ2522222-12-122-12222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-12220022-1-122-1-1-1-1-1-10022-1-1-1-1000-1-12000-1-1-1-1000002200000000-1-10
χ2622222-12-122-12222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-122-1-1-1-1222-1-1-1-1-1-12-2-20022-1-1-2-2-1-1-1-1-1-10022-1-1-1-100011-2000111100000-2-200000000110
χ2722222-12-122-12222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-22200-2-2112211111100-2-21111000-1-12000-1-1-1-100000-2-200000000110
χ2822222-12-122-12222-1-12-12-1-12-1-12-12-1-1-122-1-1-1-1-2-2-1-1-1-1222-1-1-1-1-1-1-2-2-200-2-211-2-211111100-2-2111100011-20001111000002200000000-1-10
χ2922222-12-122-12222-1-12-1-2-1-12-1-12-12-111-2-2111122-1-1-1-1-2-2-2111111-22-200-2-211221111-1-10022-1-1-1-1000-11-2000-1-111000002-200000000-110
χ3022222-12-122-12222-1-12-1-2-1-12-1-12-12-111-2-2111122-1-1-1-1-2-2-2111111-2-2200-2-211-2-21111-1-10022-1-1-1-10001-1200011-1-100000-22000000001-10
χ3122222-12-122-12222-1-12-1-2-1-12-1-12-12-111-2-21111-2-2-1-1-1-1-2-2-211111122-20022-1-122-1-1-1-11100-2-21111000-11-2000-1-11100000-22000000001-10
χ3222222-12-122-12222-1-12-1-2-1-12-1-12-12-111-2-21111-2-2-1-1-1-1-2-2-21111112-220022-1-1-2-2-1-1-1-11100-2-211110001-1200011-1-1000002-200000000-110
χ332222-12222-12-122-12-1-122-1-1-122-12-1-122-1-1-1-1-1-122-1-1-1-12-1-122-1-1-1-120022-1-12200-1-1-1-12222-1-1-1-1-1-100-10002-1-10000-1-1-1200020000-10-1000
χ342222-12222-12-122-12-1-122-1-1-122-12-1-122-1-1-1-1-1-122-1-1-1-12-1-122-1-1-1-1200-2-2-1-12200-1-1-1-122-2-2-1-1-1-1-1-1001000-2110000111-2000-20000101000
χ352222-12222-12-122-12-1-122-1-1-122-12-1-122-1-1-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-2002211-2-2001111-2-22211111100-10002-1-10000-1-1-1-2000-20000101000
χ362222-12222-12-122-12-1-122-1-1-122-12-1-122-1-1-1-1-1-1-2-2-1-1-1-12-1-122-1-1-1-1-200-2-211-2-2001111-2-2-2-2111111001000-2110000111200020000-10-1000
χ372222-12222-12-122-12-1-12-2-1-1-122-12-1-1-2-211111122-1-1-1-1-211-2-21111-2002-211-2-200111122-2-2-1-1-1-1-1-100-10002-1-10000111-200020000-101000
χ382222-12222-12-122-12-1-12-2-1-1-122-12-1-1-2-211111122-1-1-1-1-211-2-21111-200-2211-2-20011112222-1-1-1-1-1-1001000-2110000-1-1-12000-2000010-1000
χ392222-12222-12-122-12-1-12-2-1-1-122-12-1-1-2-2111111-2-2-1-1-1-1-211-2-211112002-2-1-12200-1-1-1-1-2-2-2-211111100-10002-1-100001112000-2000010-1000
χ402222-12222-12-122-12-1-12-2-1-1-122-12-1-1-2-2111111-2-2-1-1-1-1-211-2-21111200-22-1-12200-1-1-1-1-2-222111111001000-2110000-1-1-1-200020000-101000
χ4122-2-22222-22-2-2-22-2-222202-2-22-2-2-22-2000000002i−2i22-2-20000000000000000000000002i−2i002i−2i2i2i−2i−2i2-200000000000000000002-22i−2i000000
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χ4544444-2-2-2-24-24-2-24-2-2-214-2-2-211-21-2-2-2-244-2-2-2-2001111-2-2-2111111044000000-2-200000000000000000-2-2-20001111000000000000000000
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χ494444-24-24-2-24-2-2-2-24-21-24-2-21-2-21-21-244-2-2-2-2-2-2001111-211-2-2111100044000000000000-2-200000000-2000-2110000-211000000000000000
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χ534444-2-24-24-2-2-244-2-21-2-2411-2-2-2-2-2-21-2-2-2-211114411114-2-2-2-2111140000-2-2-2-2001111-2-200-2-211110000000000000000000000000000000
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χ914-4-44-24-2-4-22-4-22224-21-202-212-2-12-1200−2323−232323−23001-11-103−3003−3−330000000000000000023−230000000000000-3300000−33000000000000000
χ924-4-44-24-2-4-22-4-22224-21-202-212-2-12-1200−2323−232323−23001-11-103−3003−3−3300000000000000000−232300000000000003-3000003−3000000000000000
χ934-4-44-2-242422-2-4-42-21-2-20-11-22-2222-10023−23−333−3001-11-1023−2300−333−30000000−2i32i300i3−i3−i3i30000003i−3i−3i3i0000000000000000000000000000000
χ944-4-44-2-242422-2-4-42-21-2-20-11-22-2222-10023−23−333−3001-11-1023−2300−333−300000002i3−2i300−i3i3i3−i3000000−3i3i3i−3i0000000000000000000000000000000
χ954-4-44-2-242422-2-4-42-21-2-20-11-22-2222-100−23233−3−33001-11-10−2323003−3−330000000−2i32i300i3−i3−i3i3000000−3i3i3i−3i0000000000000000000000000000000
χ964-4-44-2-242422-2-4-42-21-2-20-11-22-2222-100−23233−3−33001-11-10−2323003−3−3300000002i3−2i300−i3i3i3−i30000003i−3i−3i3i0000000000000000000000000000000
χ978888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-4-4484-84-4-84-4-420-4442-24-2-44000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-484-4-844-44-8-42-40-44-2-44-2424000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-4-44-4444-44422202-2-22-2-2-22-200006i6i−6i−6i00-1-11100000−3i−3i3i3i00000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-4-44-4444-44422202-2-22-2-2-22-20000−6i−6i6i6i00-1-111000003i3i−3i−3i00000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-4-84484-44-4-8-42-4044-2442-4-2-400000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4444-44-44-442220-2-2-2-2-222-22−4i34i3002i3−2i32i3−2i300-111-10002i3−2i3−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444-44-44-442220-2-2-2-2-222-224i3−4i300−2i32i3−2i32i300-111-1000−2i32i3i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1068-8-888-4-44-4-84844-8-4-4-4204-4-4-224-24400000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44-444-4444-42220-222-22-2-2-2-20043−43−232323−2300-11-110−2323003−3−3300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44-444-4444-42220-222-22-2-2-2-200−434323−23−232300-11-11023−2300−333−300000000000000000000000000000000000000000000000000000000

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