Finite Group Databasebeta

← Group #13173381

Character table — Group #13173381

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112224444444444444444448888888888888888888899161616161616161616161616181818363636363636545454547272108108108108108108
order123462333333466666681224246121212121212122424242424242424242424244466666612121212121221212246824248888612448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1ii−i−i-1-1i−iii−i−i
χ41111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1−i−iii-1-1−ii−i−iii
χ5111111111111-1111111-11-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-111-1-1-11111-11-1-11-11-1
χ6111111111111-1111111-11-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1111-11-11
χ7111111111111-1111111-11-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1111ii−i−i1-1−iii−i−ii
χ8111111111111-1111111-11-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1111−i−iii1-1i−i−iii−i
χ911111-11111111111111-11-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-11-1-1-111111-1-1-1-11-11
χ1011111-11111111111111-11-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-11-1-1-1-1-1-1-11-1111-11-1
χ1111111-11111111111111-11-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1111ii−i−i-11−ii−iii−i
χ1211111-11111111111111-11-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1111−i−iii-11i−ii−i−ii
χ1311111-1111111-11111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111-1-111-1-1-1-1
χ1411111-1111111-11111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-11111
χ1511111-1111111-11111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i11i−i−i−iii
χ1611111-1111111-11111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii11−iiii−i−i
χ17222-22022222202222220-20000-2-2-2-2-2-200000000000022000000000000-22200-20002-22-200000000
χ18222-22022222202222220-20000-2-2-2-2-2-200000000000022000000000000-22200-2000-22-2200000000
χ19222-22022222202222220-20000-2-2-2-2-2-2000000000000-2-20000000000002-2-20020002i−2i−2i2i00000000
χ20222-22022222202222220-20000-2-2-2-2-2-2000000000000-2-20000000000002-2-2002000−2i2i2i−2i00000000
χ2122-12-1222-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-12-1-122-12-1-10000-1-1000000
χ2222-12-1222-1-1-1-1222-1-1-1-12-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-1-1-1-122-1-1-1-1-211-2-21-211000011000000
χ2322-12-1222-1-1-1-1-222-1-1-1-1-2-111-1122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-2-211112-1-1-22-1-21100001-1000000
χ2422-12-1222-1-1-1-1-222-1-1-1-1-2-111-1122-1-1-1-1-2-2-2-211111111-2-222-1-1-1-1-2-21111-2112-212-1-10000-11000000
χ2522-12-1-222-1-1-1-1222-1-1-1-1-2-1111-122-1-1-1-1-2-2-2-21111111122-2-2111122-1-1-1-12-1-12-2-1-2110000-11000000
χ2622-12-1-222-1-1-1-1222-1-1-1-1-2-1111-122-1-1-1-1-2-2-2-211111111-2-2-2-2111122-1-1-1-1-211-2212-1-100001-1000000
χ2722-12-1-222-1-1-1-1-222-1-1-1-12-1-1-11122-1-1-1-12222-1-1-1-1-1-1-1-122-2-21111-2-211112-1-1-2-2-12-1-1000011000000
χ2822-12-1-222-1-1-1-1-222-1-1-1-12-1-1-11122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21111-2-21111-211221-2110000-1-1000000
χ294444441-211-2-241-211-2-24444441-211-2-211-2-21111-2-2-2-2001-211-2-21-211-2-2000000000000000000000
χ304444441-211-2-2-41-211-2-2-44-4-44-41-211-2-2-1-122-1-1-1-12222001-211-2-2-12-1-122000000000000000000000
χ31444444-21-2-2114-21-2-211444444-21-2-211-2-211-2-2-2-2111100-21-2-211-21-2-211000000000000000000000
χ32444444-21-2-211-4-21-2-211-44-4-44-4-21-2-21122-1-12222-1-1-1-100-21-2-2112-122-1-1000000000000000000000
χ3344444-41-211-2-241-211-2-2-44-4-4-441-211-2-2-1-122-1-1-1-1222200-12-1-1221-211-2-2000000000000000000000
χ3444444-41-211-2-2-41-211-2-24444-4-41-211-2-211-2-21111-2-2-2-200-12-1-122-12-1-122000000000000000000000
χ3544444-4-21-2-2114-21-2-211-44-4-4-44-21-2-21122-1-12222-1-1-1-1002-122-1-1-21-2-211000000000000000000000
χ3644444-4-21-2-211-4-21-2-2114444-4-4-21-2-211-2-211-2-2-2-21111002-122-1-12-122-1-1000000000000000000000
χ3744-24-241-2−1−3i32−1+3i321141-2−1−3i32−1+3i32114-2-2-2-2-21-2−1−3i32−1+3i321111-2-2−1−3i32−1−3i32−1+3i32−1+3i321111001-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211000000000000000000000
χ3844-24-241-2−1−3i32−1+3i3211-41-2−1−3i32−1+3i3211-4-222-221-2−1−3i32−1+3i3211-1-1221+3i321+3i321−3i321−3i32-1-1-1-1001-2−1−3i32−1+3i3211-121+3i321−3i32-1-1000000000000000000000
χ3944-24-241-2−1+3i32−1−3i321141-2−1+3i32−1−3i32114-2-2-2-2-21-2−1+3i32−1−3i321111-2-2−1+3i32−1+3i32−1−3i32−1−3i321111001-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211000000000000000000000
χ4044-24-241-2−1+3i32−1−3i3211-41-2−1+3i32−1−3i3211-4-222-221-2−1+3i32−1−3i3211-1-1221−3i321−3i321+3i321+3i32-1-1-1-1001-2−1+3i32−1−3i3211-121−3i321+3i32-1-1000000000000000000000
χ4144-24-24-2111−1−3i32−1+3i324-2111−1−3i32−1+3i324-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i3200-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32000000000000000000000
χ4244-24-24-2111−1−3i32−1+3i32-4-2111−1−3i32−1+3i32-4-222-22-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i3200-2111−1−3i32−1+3i322-1-1-11+3i321−3i32000000000000000000000
χ4344-24-24-2111−1+3i32−1−3i324-2111−1+3i32−1−3i324-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i3200-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32000000000000000000000
χ4444-24-24-2111−1+3i32−1−3i32-4-2111−1+3i32−1−3i32-4-222-22-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i3200-2111−1+3i32−1−3i322-1-1-11−3i321+3i32000000000000000000000
χ4544-24-2-41-2−1−3i32−1+3i321141-2−1−3i32−1+3i3211-4-2222-21-2−1−3i32−1+3i3211-1-1221+3i321+3i321−3i321−3i32-1-1-1-100-121+3i321−3i32-1-11-2−1−3i32−1+3i3211000000000000000000000
χ4644-24-2-41-2−1−3i32−1+3i3211-41-2−1−3i32−1+3i32114-2-2-2221-2−1−3i32−1+3i321111-2-2−1−3i32−1−3i32−1+3i32−1+3i32111100-121+3i321−3i32-1-1-121+3i321−3i32-1-1000000000000000000000
χ4744-24-2-41-2−1+3i32−1−3i321141-2−1+3i32−1−3i3211-4-2222-21-2−1+3i32−1−3i3211-1-1221−3i321−3i321+3i321+3i32-1-1-1-100-121−3i321+3i32-1-11-2−1+3i32−1−3i3211000000000000000000000
χ4844-24-2-41-2−1+3i32−1−3i3211-41-2−1+3i32−1−3i32114-2-2-2221-2−1+3i32−1−3i321111-2-2−1+3i32−1+3i32−1−3i32−1−3i32111100-121−3i321+3i32-1-1-121−3i321+3i32-1-1000000000000000000000
χ4944-24-2-4-2111−1−3i32−1+3i324-2111−1−3i32−1+3i32-4-2222-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32002-1-1-11+3i321−3i32-2111−1−3i32−1+3i32000000000000000000000
χ5044-24-2-4-2111−1−3i32−1+3i32-4-2111−1−3i32−1+3i324-2-2-222-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32002-1-1-11+3i321−3i322-1-1-11+3i321−3i32000000000000000000000
χ5144-24-2-4-2111−1+3i32−1−3i324-2111−1+3i32−1−3i32-4-2222-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32002-1-1-11−3i321+3i32-2111−1+3i32−1−3i32000000000000000000000
χ5244-24-2-4-2111−1+3i32−1−3i32-4-2111−1+3i32−1−3i324-2-2-222-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32002-1-1-11−3i321+3i322-1-1-11−3i321+3i32000000000000000000000
χ5344-2-4-2044-2-2-2-2044-2-2-2-2020000-4-4222200000000000044000000000000-4-2-2002000000000000000
χ5444-2-4-2044-2-2-2-2044-2-2-2-2020000-4-42222000000000000-4-400000000000042200-2000000000000000
χ554-440-404444440-4-4-4-4-4-40000000000000000000000004i−4i00000000000004i−4i000000000000000000
χ564-440-404444440-4-4-4-4-4-4000000000000000000000000−4i4i0000000000000−4i4i000000000000000000
χ574-4-202044-2-2-2-20-4-42222006−60000000000006−66−66−66−64i−4i0000000000000−2i2i0000i6−i6000000000000
χ584-4-202044-2-2-2-20-4-42222006−60000000000006−66−66−66−6−4i4i00000000000002i−2i0000−i6i6000000000000
χ594-4-202044-2-2-2-20-4-4222200−66000000000000−66−66−66−664i−4i0000000000000−2i2i0000−i6i6000000000000
χ604-4-202044-2-2-2-20-4-4222200−66000000000000−66−66−66−66−4i4i00000000000002i−2i0000i6−i6000000000000
χ61888-8802-422-4-402-422-4-40-80000-24-2-24400000000000000000000000000000000000000000000000
χ62888-880-42-4-4220-42-4-4220-800004-244-2-200000000000000000000000000000000000000000000000
χ6388-4-8-402-4−1−3i3−1+3i32202-4−1−3i3−1+3i322040000-241+3i31−3i3-2-200000000000000000000000000000000000000000000000
χ6488-4-8-402-4−1+3i3−1−3i32202-4−1+3i3−1−3i322040000-241−3i31+3i3-2-200000000000000000000000000000000000000000000000
χ6588-4-8-40-4222−1−3i3−1+3i30-4222−1−3i3−1+3i30400004-2-2-21+3i31−3i300000000000000000000000000000000000000000000000
χ6688-4-8-40-4222−1+3i3−1−3i30-4222−1+3i3−1−3i30400004-2-2-21−3i31+3i300000000000000000000000000000000000000000000000
χ678-880-802-422-4-40-24-2-244000000000000−3i23i200−3i23i23i2−3i2000000000000000000000000000000000000000
χ688-880-802-422-4-40-24-2-2440000000000003i2−3i2003i2−3i2−3i23i2000000000000000000000000000000000000000
χ698-880-80-42-4-42204-244-2-200000000000000−3i23i20000−3i23i23i2−3i200000000000000000000000000000000000
χ708-880-80-42-4-42204-244-2-2000000000000003i2−3i200003i2−3i2−3i23i200000000000000000000000000000000000
χ718-8-40402-4−1−3i3−1+3i3220-241+3i31−3i3-2-20026−26000000003i2−3i200−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ232ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ23−66−6600000000000000000000000000000000000
χ728-8-40402-4−1−3i3−1+3i3220-241+3i31−3i3-2-200−262600000000−3i23i200ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ23−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ236−66−600000000000000000000000000000000000
χ738-8-40402-4−1+3i3−1−3i3220-241−3i31+3i3-2-20026−2600000000−3i23i2002ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ23−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ23−66−6600000000000000000000000000000000000
χ748-8-40402-4−1+3i3−1−3i3220-241−3i31+3i3-2-200−2626000000003i2−3i200−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ23ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ236−66−600000000000000000000000000000000000
χ758-8-4040-4222−1−3i3−1+3i304-2-2-21+3i31−3i30026−2600000000003i2−3i2−66−66−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ232ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ2300000000000000000000000000000000000
χ768-8-4040-4222−1−3i3−1+3i304-2-2-21+3i31−3i300−26260000000000−3i23i26−66−6ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ23−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ2300000000000000000000000000000000000
χ778-8-4040-4222−1+3i3−1−3i304-2-2-21−3i31+3i30026−260000000000−3i23i2−66−662ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ23−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ2300000000000000000000000000000000000
χ788-8-4040-4222−1+3i3−1−3i304-2-2-21−3i31+3i300−262600000000003i2−3i26−66−6−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ23ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ2300000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.