Finite Group Databasebeta

← Group #13172100

Character table — Group #13172100

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order122233366666666623336666666666644366666666666666622444661212121212122244444466666661212121212121212121212121244661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-11111-1-111-1-1-1-1-1-1111-1-111-1-111-111111111-1-11-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-11-1-111111111-1-1-1-1-1-1-111-1-1111-111-11111-1-111-1111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11-11111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-11111-1-111-1-1-1-11111-1-11111111-111-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-1-11-1-11-1-1-1-111-1-1-1111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-111-1-1-1-1-1-1-1-111-111-1-111-1-11-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111-1-111-1-111-1-1111111111-1-1-1-1-111-1-1-1-1-1-1-11-1-11111-1-111-11-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111111111-1-111111-1-111-1-1-1-11-1-111-1-1-1-111-1-11111-1-111-1-1-1-11
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-111-1-111-1-1-1-111-1-1-111-1-111-11-1-1111-1-111-1-111-1-1-1-1-1-111-1-1111
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-111111-111-1-111-1-1111-1-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-11-1-1-111-1-1-1-11-111-1-111-1-1-1-11-11
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111-1-111-1-1-1-1-1-111-1-11-1-111-1-11-111-1-1-111-1-11111-1-1-1-1-1-1111111-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-11111-111-1-11111-111-1-11111-1-1-1-11111-1-11111-1-1-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-111111-1-1111111-11-1-11111-1-1-1-1-111
χ17222222-12-122-12-1222-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10220200-1-1-1-1222200000002-100-1-1202-10-1-1-1-100-1-102-1-1000000000-10
χ18222222-12-122-12-1222-12-122-122-1-1-1-12-122-12-1-1-122-1-1-1-1-1-1-1-1-10-220-200-1-11122-2-20000000-21001120-2-10-1-1-1-100110-21100000000010
χ19222222-12-122-12-1222-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-102-2020011-1-1-2-2-2-200000002-100-1-1-20210111100-1-10-21100000000010
χ20222222-12-122-12-1222-12-122-122-1-1-1-12-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-10-2-20-2001111-2-2220000000-210011-20-2101111001102-1-1000000000-10
χ21222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-1111102-20-200-1-11122-2-200000002-100-1-1-20-210-1-11100110211000000000-10
χ22222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-122-1-2111-2-211-1-1-111110-2-20200-1-1-1-122220000000-210011-20210-1-11100-1-10-2-1-100000000010
χ23222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110220-2001111-2-22200000002-100-1-120-2-1011-1-100110-2-1-100000000010
χ24222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-2-2-1-2111-2-211-1-1-111110-22020011-1-1-2-2-2-20000000-210011202-1011-1-100-1-10211000000000-10
χ2522222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1220222200220000222200-1-12-1-1-1-10-1-1020000-1-1-1-1000000-1-1-1-100000
χ2622222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-202-22200-2-20000-2-2-2-200-11-2-1-1110-11020000-1-111000000111100000
χ2722222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-220-22-2-200220000-2-2-2-2001-1211-1-101-10-2000011-1-1000000111100000
χ2822222-12-122-12222-122-1-1-1-12-1-1-1-122-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-200-2-2000022220011-211110110-200001111000000-1-1-1-100000
χ2922222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111220-2-22200-2-2000022-2-200-1-12-1-1-1-10110-200001111000000-1-11100000
χ3022222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-111112-20-222200220000-2-22200-11-2-1-11101-10-2000011-1-100000011-1-100000
χ3122222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2202-2-2-200-2-20000-2-222001-1211-1-10-11020000-1-11100000011-1-100000
χ3222222-12-122-12222-1-22-1-1112-1-1-1-122-1-100-1-2-2-2-21111-1-1-11111-2-2022-2-20022000022-2-20011-211110-1-1020000-1-1-1-1000000-1-11100000
χ332222-12222-122-12-122-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-120220-1-12200-1-100000022200-1-100-1202-1-1-1-1-1-1-1002000-1-1000000-100
χ342222-12222-122-12-122-1-1222-1-1-122-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1-202-20112200-1-1000000-2-2-2001100-1-2021-1-1-1-11100-200011000000100
χ352222-12222-122-12-122-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-120-220-1-1-2-20011000000-2-2200-1-100120-2-11111-1-100-200011000000100
χ362222-12222-122-12-122-1-1222-1-1-122-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-2011-2-2001100000022-20011001-20-21111111002000-1-1000000-100
χ372222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-1111120-2-20-1-12200-1-100000022200-1-1001-20-21-1-1111100-2000-1-1000000100
χ382222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-1222-11-21111-2-2-1-1-11111-20-220112200-1-1000000-2-2-2001100120-2-1-1-111-1-100200011000000-100
χ392222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111202-20-1-1-2-20011000000-2-2200-1-100-1-202111-1-11100200011000000-100
χ402222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-2-2-11-21111-2-2-1-1-11111-2022011-2-2001100000022-2001100-1202-111-1-1-1-100-2000-1-1000000100
χ4122-2-2222-22-2-2-22-2-2202220022-22-2-2-2-2-22i−2i2000000002-2-2000000000002i−2i002i−2i002-200000000000000002i−2i0000000000002-2002i−2i000
χ4222-2-2222-22-2-2-22-2-2202220022-22-2-2-2-2-22i−2i2000000002-2-2000000000002i−2i002i−2i00-2200000000000000002i−2i000000000000-2200−2i2i000
χ4322-2-2222-22-2-2-22-2-2202220022-22-2-2-2-2-2−2i2i2000000002-2-200000000000−2i2i00−2i2i002-20000000000000000−2i2i0000000000002-200−2i2i000
χ4422-2-2222-22-2-2-22-2-2202220022-22-2-2-2-2-2−2i2i2000000002-2-200000000000−2i2i00−2i2i00-220000000000000000−2i2i000000000000-22002i−2i000
χ452-22-22222-22-2-2-22-2-2022200-2-22-222-2-2-200200000000-22-2000000000000000002-2002i−2i2i−2i00000000000000000000002-22i−2i002i−2i00000
χ462-22-22222-22-2-2-22-2-2022200-2-22-222-2-2-200200000000-22-2000000000000000002-200−2i2i−2i2i00000000000000000000002-2−2i2i00−2i2i00000
χ472-22-22222-22-2-2-22-2-2022200-2-22-222-2-2-200200000000-22-200000000000000000-22002i−2i−2i2i0000000000000000000000-22−2i2i002i−2i00000
χ482-22-22222-22-2-2-22-2-2022200-2-22-222-2-2-200200000000-22-200000000000000000-2200−2i2i2i−2i0000000000000000000000-222i−2i00−2i2i00000
χ4944444-2-2-2-24-2-24-24-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-2111111111040040000-2-200000000000-2-2001100-20000000011000000000000000
χ5044444-2-2-2-24-2-24-24-24-2-21-2-2-2-2-211-2-2-210014-2-2-2-2-21111111110-400-4000022000000000002200-1-100200000000-1-1000000000000000
χ5144444-2-2-2-24-2-24-24-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10400-400002200000000000-2-2001100200000000-1-1000000000000000
χ5244444-2-2-2-24-2-24-24-2-4-2-2122-2-2-211-2-2-21001-422222-1-1111-1-1-1-10-40040000-2-2000000000002200-1-100-20000000011000000000000000
χ534444-24-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-2441-2-211-2-2-2-211111110040000-2-200-2-2000000000000000-200-2011110000000000000000000
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χ554444-24-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-244122-1-12222111-1-1-1-100-40000-2-200-2-20000000000000002002011-1-10000000000000000000
χ564444-24-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2-4-4122-1-12222111-1-1-1-10040000220022000000000000000-200-20-1-1110000000000000000000
χ574444-2-24-24-2-24-24-2-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-2111111140040-2-200000000000000-20011000-200-200001100000000000000000
χ584444-2-24-24-2-24-24-2-24-21-2-2-2-211-2-2-2-21-2001-24-2-211-2-21111111-400-402200000000000000200-1-100020020000-1-100000000000000000
χ594444-2-24-24-2-24-24-2-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-1400-40-2-200000000000000-2001100020020000-1-100000000000000000
χ604444-2-24-24-2-24-24-2-2-4-21-222-211-2-2-2-21-20012-422-1-122111-1-1-1-1-400402200000000000000200-1-1000-200-200001100000000000000000
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χ6944-4-4-24-2-4-22-42-222401-2-2001-22-22-1-122−4i4i1003-300001-1-133-3-300000002i−2i002i−2i00000000000000000000−ii−3i3i0000000000000000000
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χ1008-88-8-4-48-4-8-44-848440-42-4004-224-4-44-2400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4-44-4444-444022200-2-22-222-2-2-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-44-4444-444022200-2-22-222-2-2-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ1038-8-88-48-4-8448-444-4-802-4-400-24444-22-4-400200000000-2-22000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4444-4-444-440222−4i34i3-2-2-2-2-2-222200-100002i3−2i32i3−2i311-1−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4444-4-444-4402224i3−4i3-2-2-2-2-2-222200-10000−2i32i3−2i32i311-1i3−i3i3−i300000000000000000000000000000000000000000000000000000000

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