Finite Group Databasebeta

← Group #13049541

Character table — Group #13049541

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1122222222334444444444444444666666888888888812121212121212121212181818181818181818363636363636363636545454545454545454
order1233336666443333333366666666121212121212333336666612121212121212121212224666612126666661212122446612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11-111-1-1-1-1-1-11-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111-11-1-1-111-1-1-11-1-111-1-1-1-1-11-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1
χ51111111111-1-11111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ61111111111-1-11111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11-111-1-1-1-1-11-1111-1-111
χ71111111111-1-11111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-11-1-111-1-1-111-11111-1-1
χ81111111111-1-11111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1111-111-1-11111
χ922222-12-122222-1-1-1-1-122222-1-1-1-1-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10020000-1-10000002-1-1200-1-10000
χ1022222-12-122222-1-1-1-1-122222-1-1-1-1-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-100-2000011000000-211-200110000
χ1122222-12-122-2-22-1-1-1-1-122222-1-1-1-1-111-2-2-2-22-1-1-1-12-1-1-1-1-2-2111111110020000-1-10000002-1-1-200110000
χ1222222-12-122-2-22-1-1-1-1-122222-1-1-1-1-111-2-2-2-22-1-1-1-12-1-1-1-1-2-21111111100-2000011000000-211200-1-10000
χ132222-12-12220022222-1-1-1-1-122222-1000000-1-1-1-1-1-1-1-1-1-10000000000222222222-1-1-1-1-1-1-1-1-1000000000
χ142222-12-12220022222-1-1-1-1-122222-1000000-1-1-1-1-1-1-1-1-1-100000000002-2-222-2-2-2-2-11-1-111111000000000
χ152222-12-12220022222-1-1-1-1-122222-1000000-1-1-1-1-1-1-1-1-1-10000000000-22-2-2-222-2-21-111-1-1111000000000
χ162222-12-12220022222-1-1-1-1-122222-1000000-1-1-1-1-1-1-1-1-1-10000000000-2-22-2-2-2-222111111-1-1-1000000000
χ17222-122222-122-12-1-1-122-12-1-12-1-1-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-102000-1-1000200-1-10000020000-1-1
χ18222-122222-122-12-1-1-122-12-1-12-1-1-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-10-200011000-2001100000-2000011
χ19222-122222-1-2-2-12-1-1-122-12-1-12-1-1-12-2-2-2-211-12-1-1-1-12-1-1-111-2-211111102000-1-1000200-1-100000-2000011
χ20222-122222-1-2-2-12-1-1-122-12-1-12-1-1-12-2-2-2-211-12-1-1-1-12-1-1-111-2-21111110-200011000-200110000020000-1-1
χ2122-122222-1222-1-12-1-12-12-12-1-12-1-1222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1200-1-1000020-1-10000002000-1-100
χ2222-122222-1222-1-12-1-12-12-12-1-12-1-1222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-200110000-2011000000-20001100
χ2322-122222-12-2-2-1-12-1-12-12-12-1-12-1-12-2-211-2-2-1-12-1-1-1-12-1-11111-2-21111200-1-1000020-1-1000000-20001100
χ2422-122222-12-2-2-1-12-1-12-12-12-1-12-1-12-2-211-2-2-1-12-1-1-1-12-1-11111-2-21111-200110000-20110000002000-1-100
χ252-22222-2-2-2-22i−2i22222222-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i22222-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i000000000000000000000000000
χ262-22222-2-2-2-2−2i2i22222222-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i22222-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i000000000000000000000000000
χ272-2222-1-21-2-22i−2i2-1-1-1-1-122-2-2-211111−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00000003−300000003−3000−i3i30000
χ282-2222-1-21-2-22i−2i2-1-1-1-1-122-2-2-211111−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii0000000−330000000−33000i3−i30000
χ292-2222-1-21-2-2−2i2i2-1-1-1-1-122-2-2-211111i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00000003−300000003−3000i3−i30000
χ302-2222-1-21-2-2−2i2i2-1-1-1-1-122-2-2-211111i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i0000000−330000000−33000−i3i30000
χ312-22-122-2-2-212i−2i-12-1-1-122-1-211-2111-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000−i3i3000000−i3i300000000003−3
χ322-22-122-2-2-212i−2i-12-1-1-122-1-211-2111-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000i3−i3000000i3−i30000000000−33
χ332-22-122-2-2-21−2i2i-12-1-1-122-1-211-2111-2−2i2i−2i2ii−i-12-1-1-11-2111i−i−2i2ii−iii−i−i00000−i3i3000000−i3i30000000000−33
χ342-22-122-2-2-21−2i2i-12-1-1-122-1-211-2111-2−2i2i−2i2ii−i-12-1-1-11-2111i−i−2i2ii−iii−i−i00000i3−i3000000i3−i300000000003−3
χ352-2-1222-2-21-22i−2i-1-12-1-12-121-211-211-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii000−i3i3000000−i3i300000000003−300
χ362-2-1222-2-21-22i−2i-1-12-1-12-121-211-211-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii000i3−i3000000i3−i30000000000−3300
χ372-2-1222-2-21-2−2i2i-1-12-1-12-121-211-211-2−2i2ii−i−2i2i-1-12-1-111-211i−ii−i−2i2iii−i−i000−i3i3000000−i3i30000000000−3300
χ382-2-1222-2-21-2−2i2i-1-12-1-12-121-211-211-2−2i2ii−i−2i2i-1-12-1-111-211i−ii−i−2i2iii−i−i000i3−i3000000i3−i300000000003−300
χ394444-2-2-2-244004-2-2-2-21-2-2-2-24-2-2-2-21000000-21111-2111100000000000040000-2-2000000-211000000000
χ404444-2-2-2-244004-2-2-2-21-2-2-2-24-2-2-2-21000000-21111-21111000000000000-40000220000002-1-1000000000
χ41444-24-24-24-244-2-2111-24-24-2-2-2111-2-2-244-2-2-2-2111-2-2111-2-2-2-2111111000000000000000000000000000
χ42444-24-24-24-2-4-4-2-2111-24-24-2-2-2111-222-4-422-2-2111-2-21112222-1-1-1-1-1-1000000000000000000000000000
χ43444-2-24-244-200-24-2-2-2-2-21-21-24-2-2-2-20000001-21111-2111000000000004000-2-2000-20011000000000000
χ44444-2-24-244-200-24-2-2-2-2-21-21-24-2-2-2-20000001-21111-211100000000000-400022000200-1-1000000000000
χ4544-244-24-2-2444-21-211-2-24-24-21-211-2-2-2-2-244-21-211-21-211-2-211-2-21111000000000000000000000000000
χ4644-244-24-2-24-4-4-21-211-2-24-24-21-211-22222-4-4-21-211-21-21122-1-122-1-1-1-1000000000000000000000000000
χ4744-24-24-24-2400-2-24-2-2-21-21-2-2-24-2-2-200000011-21111-2110000000000400-2-20000-201100000000000000
χ4844-24-24-24-2400-2-24-2-2-21-21-2-2-24-2-2-200000011-21111-2110000000000-40022000020-1-100000000000000
χ4944-2-24444-2-2441-2-2114-2-2-2-21-2-211444-2-2-2-21-2-2111-2-21111-2-2-2-21111000000000000000000000000000
χ5044-2-24444-2-2-4-41-2-2114-2-2-2-21-2-2114-4-422221-2-2111-2-211-1-12222-1-1-1-1000000000000000000000000000
χ5144-2-24-24-2-2-244111−1−3i32−1+3i32-2-2-2-2-2111−1−3i32−1+3i32-2-2-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000
χ5244-2-24-24-2-2-244111−1+3i32−1−3i32-2-2-2-2-2111−1+3i32−1−3i32-2-2-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ5344-2-24-24-2-2-2-4-4111−1−3i32−1+3i32-2-2-2-2-2111−1−3i32−1+3i32-2222222111−1−3i32−1+3i32111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
χ5444-2-24-24-2-2-2-4-4111−1+3i32−1−3i32-2-2-2-2-2111−1+3i32−1−3i32-2222222111−1+3i32−1−3i32111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000
χ554-444-242-4-4-40044444-2-2-222-4-4-4-4-42000000-2-2-2-2-2222220000000000000000000000000000000000000
χ564-444-2-222-4-4004-2-2-2-21-2-222-42222-1000000-211112-1-1-1-10000000000000000023−230000000−33000000000
χ574-444-2-222-4-4004-2-2-2-21-2-222-42222-1000000-211112-1-1-1-100000000000000000−232300000003−3000000000
χ584-44-24-2-42-424i−4i-2-2111-24-2-4222-1-1-12−2i2i4i−4i−2i2i-2-211122-1-1-1−2i2i−2i2ii−iii−i−i000000000000000000000000000
χ594-44-24-2-42-42−4i4i-2-2111-24-2-4222-1-1-122i−2i−4i4i2i−2i-2-211122-1-1-12i−2i2i−2i−ii−i−iii000000000000000000000000000
χ604-44-2-242-4-4200-24-2-2-2-2-212-12-422220000001-2111-12-1-1-1000000000000000−2i32i3000000i3−i3000000000000
χ614-44-2-242-4-4200-24-2-2-2-2-212-12-422220000001-2111-12-1-1-10000000000000002i3−2i3000000−i3i3000000000000
χ624-4-244-2-422-44i−4i-21-211-2-242-42-12-1-12−2i2i−2i2i4i−4i-21-2112-12-1-1−2i2ii−i−2i2iii−i−i000000000000000000000000000
χ634-4-244-2-422-4−4i4i-21-211-2-242-42-12-1-122i−2i2i−2i−4i4i-21-2112-12-1-12i−2i−ii2i−2i−i−iii000000000000000000000000000
χ644-4-24-242-42-400-2-24-2-2-21-2-1222-422200000011-211-1-12-1-10000000000000−2i32i3000000i3−i300000000000000
χ654-4-24-242-42-400-2-24-2-2-21-2-1222-422200000011-211-1-12-1-100000000000002i3−2i3000000−i3i300000000000000
χ664-4-2-244-4-4224i−4i1-2-2114-2-222-122-1-1-44i−4i−2i2i−2i2i1-2-211-122-1-1i−i−2i2i−2i2iii−i−i000000000000000000000000000
χ674-4-2-244-4-422−4i4i1-2-2114-2-222-122-1-1-4−4i4i2i−2i2i−2i1-2-211-122-1-1−ii2i−2i2i−2i−i−iii000000000000000000000000000
χ684-4-2-24-2-42224i−4i111−1−3i32−1+3i32-2-2-222-1-1-11+3i321−3i322−2i2i−2i2i−2i2i111−1−3i32−1+3i32-1-1-11+3i321−3i32i−ii−ii−i−ζ7+2ζ112ζ7−ζ11ζ7−2ζ11−2ζ7+ζ11000000000000000000000000000
χ694-4-2-24-2-42224i−4i111−1+3i32−1−3i32-2-2-222-1-1-11−3i321+3i322−2i2i−2i2i−2i2i111−1+3i32−1−3i32-1-1-11−3i321+3i32i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ11000000000000000000000000000
χ704-4-2-24-2-4222−4i4i111−1−3i32−1+3i32-2-2-222-1-1-11+3i321−3i3222i−2i2i−2i2i−2i111−1−3i32−1+3i32-1-1-11+3i321−3i32−ii−ii−iiζ7−2ζ11−2ζ7+ζ11−ζ7+2ζ112ζ7−ζ11000000000000000000000000000
χ714-4-2-24-2-4222−4i4i111−1+3i32−1−3i32-2-2-222-1-1-11−3i321+3i3222i−2i2i−2i2i−2i111−1+3i32−1−3i32-1-1-11−3i321+3i32−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11000000000000000000000000000
χ72888-4-4-4-4-48-400-4-42222-42-42-4-4222200000022-1-1-122-1-1-10000000000000000000000000000000000000
χ7388-48-4-4-4-4-4800-42-42222-42-4-42-42220000002-12-1-12-12-1-10000000000000000000000000000000000000
χ7488-4-4-48-48-4-4002-4-422-422222-4-422-4000000-122-1-1-122-1-10000000000000000000000000000000000000
χ7588-4-4-4-4-4-4-4-400222−1−3i3−1+3i322222222−1−3i3−1+3i32000000-1-1-11+3i321−3i32-1-1-11+3i321−3i320000000000000000000000000000000000000
χ7688-4-4-4-4-4-4-4-400222−1+3i3−1−3i322222222−1+3i3−1−3i32000000-1-1-11−3i321+3i32-1-1-11−3i321+3i320000000000000000000000000000000000000
χ778-88-4-4-444-8400-4-42222-424-244-2-2-2-200000022-1-1-1-2-21110000000000000000000000000000000000000
χ788-8-48-4-4444-800-42-42222-4-244-24-2-2-20000002-12-1-1-21-2110000000000000000000000000000000000000
χ798-8-4-4-484-844002-4-422-422-2-2-244-2-24000000-122-1-11-2-2110000000000000000000000000000000000000
χ808-8-4-4-4-4444400222−1−3i3−1+3i3222-2-2-2-2-21+3i31−3i3-2000000-1-1-11+3i321−3i32111−1−3i32−1+3i320000000000000000000000000000000000000
χ818-8-4-4-4-4444400222−1+3i3−1−3i3222-2-2-2-2-21−3i31+3i3-2000000-1-1-11−3i321+3i32111−1+3i32−1−3i320000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.