Finite Group Databasebeta

← Group #13168659

Character table — Group #13168659

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222444444444444466668888888888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363636363636363654545454727272
order122233366666666633346666666664444366612121212121212121212121212244412121212121212121212121244446666121212121212121212121212121244441212121212122244121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-1-1-1-1-111111111-1-1-1-111111-1-1111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111-1-11111111111111111111-11111111-1-111-1-111-1-11111-111-1111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11
χ41111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11111-11-1
χ511111111111111111111111111111-1-11111111111111111111-11111111-1-111-1-111-1-111-1-1-1-11111-1-111111111-1-11-1-1-111-1-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111-11-1-1-1-1-1-1111111-1-11
χ711111111111111111111111111111-1-1-1-111111111111111111-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11-1-1111-1-1-1-111111-1-1
χ811111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111
χ91111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111111111-1-111-1-1-1-1-11-1-11111-1-111-1-1-11-111111-1-111-1-1-1-11
χ101111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-111-1-111-11-1
χ111111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-111111-1-1-1-111111-1-1-1-1-1-1-1-1-111111
χ121111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-11-11111-1-111-1-1111-1-1-1-1-1111111-1-11-1-1
χ131111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111111111-11-1-1-1-111-1-111-1-11-1-1-1-1-11111-1-1111-1-1
χ141111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-111-1-1-1-11111-1-11-1-1-1-1-11111-1-1111-1-1-1-1-1-1-111-1-1111
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1-111-1-1111111-11-1-111-1-1-1-111-1-11111-1-11111-1-1-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-111-1-111-11-111111-1-1-1-111-1-11
χ17222222-1222-1-1-12222-1-122-1-1-1-12-12-12222-1-1-1-12-12-1-1-1-122-1-1-1-12020000022-1-1-1-12200002-1-1-1-1002-1-10000-1-1-1-12002-1-100000000-100
χ18222222-1222-1-1-12222-1-122-1-1-1-12-12-122-2-2-1-1-1-12-12-1-1-1-122-1-1-1-120-2000002211-1-1-2-200002-1-1-1100-2-1-100001111-200-21100000000100
χ19222222-1222-1-1-12222-1-122-1-1-1-12-12-1-2-222-1-1-1-12-12-1-1-1-122-1-1-1-1-20200000-2-2-1-111220000-2111-1002110000-1-1-1-1-200-21100000000100
χ20222222-1222-1-1-12222-1-122-1-1-1-12-12-1-2-2-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1-20-200000-2-21111-2-20000-2111100-211000011112002-1-100000000-100
χ21222222-1222-1-1-12222-1-1-22-1-1-1-12-12-12222-1-1-1-1-21-21111-2-21111-20-20000022-1-1-1-1220000-2111100-2-1-10000-1-111-2002-1-100000000100
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χ23222222-1222-1-1-12222-1-1-22-1-1-1-12-12-1-2-222-1-1-1-1-21-21111-2-2111120-200000-2-2-1-1112200002-1-1-1100-2110000-1-111200-21100000000-100
χ24222222-1222-1-1-12222-1-1-22-1-1-1-12-12-1-2-2-2-2-1-1-1-1-21-21111-2-2111120200000-2-21111-2-200002-1-1-1-100211000011-1-1-2002-1-100000000100
χ2522222-122-1-122222-1-12-12-12-12-1-1-1-122200-1-1-1-1-12222-1-1-1-1-1-1-1-1220222-1-1-1-10022002200-12-1-10-120-1-1-1-1-1-1000002000000-1-1000000-1
χ2622222-122-1-122222-1-12-12-12-12-1-1-1-122200-1-1-1-1-12222-1-1-1-1-1-1-1-12-20-2-2-211-1-1002200-2-200-12-1-101-20-1-1111100000-2000000110000001
χ2722222-122-1-122222-1-12-12-12-12-1-1-1-12-2-200-1-1-1-1-12222-1-1-1-1-1-1-1-1-220222-1-11100-2-200-2-2001-2110-12011-1-1-1-100000-2000000110000001
χ2822222-122-1-122222-1-12-12-12-12-1-1-1-12-2-200-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-20-2-2-2111100-2-20022001-21101-20111111000002000000-1-1000000-1
χ2922222-122-1-122222-1-12-1-2-12-12-1-1-1-122200-1-1-1-11-2-2-2-211111111-220-22211-1-1002200-2-2001-2110-1-20-1-1-1-11100000200000011000000-1
χ3022222-122-1-122222-1-12-1-2-12-12-1-1-1-122200-1-1-1-11-2-2-2-211111111-2-202-2-2-1-1-1-100220022001-2110120-1-111-1-100000-2000000-1-10000001
χ3122222-122-1-122222-1-12-1-2-12-12-1-1-1-12-2-200-1-1-1-11-2-2-2-211111111220-222111100-2-2002200-12-1-10-1-2011-1-11100000-2000000-1-10000001
χ3222222-122-1-122222-1-12-1-2-12-12-1-1-1-12-2-200-1-1-1-11-2-2-2-2111111112-202-2-2-1-11100-2-200-2-200-12-1-101201111-1-100000200000011000000-1
χ332222-122-122222-1-12-1-122-1-12-12-12-1-10022-1-1-1-122-1-1-122-1-1-1-1-1-10222-1-122002200-1-10022000022-1-100-1-1-1-1-1-1-1-1002000-1-10000000-10
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χ352222-122-122222-1-12-1-122-1-12-12-12-1-100-2-2-1-1-1-122-1-1-122-1-1-1-1-1-102-22-1-12200-2-2001100-2-20000-22-1100-1-1-1-1111100-200011000000010
χ362222-122-122222-1-12-1-122-1-12-12-12-1-100-2-2-1-1-1-122-1-1-122-1-1-1-1-1-10-2-2-211-2-200-2-2001100220000-2-2110011111111002000-1-10000000-10
χ372222-122-122222-1-12-1-12-2-1-12-12-12-1-10022-1-1-1-1-2-2111-2-211111102-2-2-1-1-2-2002200-1-100220000-221100-1-111-1-11100-2000-1-1000000010
χ382222-122-122222-1-12-1-12-2-1-12-12-12-1-10022-1-1-1-1-2-2111-2-21111110-2-221122002200-1-100-2-20000-2-2-110011-1-1-1-111002000110000000-10
χ392222-122-122222-1-12-1-12-2-1-12-12-12-1-100-2-2-1-1-1-1-2-2111-2-2111111022-2-1-1-2-200-2-2001100-2-20000221-100-1-11111-1-1002000110000000-10
χ402222-122-122222-1-12-1-12-2-1-12-12-12-1-100-2-2-1-1-1-1-2-2111-2-21111110-222112200-2-20011002200002-2-1-10011-1-111-1-100-2000-1-1000000010
χ412-22-2222-2-2-22-2-2-22222202-22-2-2-2-2-222i−2i0022-2-20000000000000000000002i−2i002i−2i00002i−2i000000002i−2i000000000000002i−2i002-200000
χ422-22-2222-2-2-22-2-2-22222202-22-2-2-2-2-222i−2i0022-2-20000000000000000000002i−2i002i−2i0000−2i2i000000002i−2i00000000000000−2i2i00-2200000
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χ452-2-22222-22-2-22-22-2-22220-2-2-222-2-22-2002i−2i2-2-22000000000000000000000002i−2i002i−2i2i−2i00000000000000002i−2i00000000002i−2i002-2000
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χ1018-88-8-4-4-4444-4444-4-422202-22-2-2-2-2-220000-1-11100000−6i6i003i−3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1028-8-888-4-4-8-444-448-84-4-42044-2-424-2-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-484-44-88-8-4442-4-40-244-4-4-242400002-2-2200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44-444-44-4442220-2-2-222-2-22-20000-111-10006-60000-333-30000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44-444-44-4442220-2-2-222-2-22-20000-111-1000-6600003-3-330000000000000000000000000000000000000000000000000000000

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