Finite Group Databasebeta

← Group #13146378

Character table — Group #13146378

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222666666121212121818242424242424363636363636363636363636363636364848484854547272727272727272
order1244361212234612126612128836612121224448888121212122424242436121288612242424242424
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ3111111111111111111-1-111111111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1
χ4111111111111111111-1-1111111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1
χ511-1-111-1-1-1111-1-1-1-111i−i1-111-1-11-1i−ii−i1-1ii−i−i11-1-111-1-1i−i1-1i−iii−i−i
χ611-1-111-1-1-1111-1-1-1-111i−i1-111-1-1-11−ii−ii-11−i−iii-1-11111-1-1i−i-11−iiii−i−i
χ711-1-111-1-1-1111-1-1-1-111−ii1-111-1-11-1−ii−ii1-1−i−iii11-1-111-1-1−ii1-1−ii−i−iii
χ811-1-111-1-1-1111-1-1-1-111−ii1-111-1-1-11i−ii−i-11ii−i−i-1-11111-1-1−ii-11i−i−i−iii
χ922222222222222222222-12-12-1-10000000000000000-1-1-1-1220000-1-1-1-1
χ10222222222222222222-2-2-12-12-1-10000000000000000-1-1-1-1-2-200001111
χ11222222222-12-1-1-1-122-1002-12-122220000220000-1-1-1-1-1-1-1-100-1-1000000
χ12222222222-12-1-1-1-122-1002-12-122-2-20000-2-200001111-1-1-1-10011000000
χ1322-2-222-2-2-2222-2-2-2-2222i−2i-1-2-12110000000000000000-1-1112i−2i0000−i−iii
χ1422-2-222-2-2-2222-2-2-2-222−2i2i-1-2-12110000000000000000-1-111−2i2i0000ii−i−i
χ1522-2-222-2-2-2-12-1111-22-100212-1-2-22-200002-20000-1-111-1-11100-11000000
χ1622-2-222-2-2-2-12-1111-22-100212-1-2-2-220000-22000011-1-1-1-111001-1000000
χ1733333333-13-1333-1-1-1-1330-10-10011-1-111-1-1-1-1-1-1-1-1-1-10000-1-111110000
χ1833333333-13-1333-1-1-1-1330-10-100-1-111-1-111111111110000-1-1-1-1-1-10000
χ1933333333-13-1333-1-1-1-1-3-30-10-1001111-1-1-1-11111-1-1-1-100001111-1-10000
χ2033333333-13-1333-1-1-1-1-3-30-10-100-1-1-1-11111-1-1-1-11111000011-1-1110000
χ2133-3-333-3-313-13-3-311-1-13i−3i010-1001-1−iii−i-11−i−iii-1-1110000−ii1-1i−i0000
χ2233-3-333-3-313-13-3-311-1-13i−3i010-100-11i−i−ii1-1ii−i−i11-1-10000−ii-11−ii0000
χ2333-3-333-3-313-13-3-311-1-1−3i3i010-1001-1i−i−ii-11ii−i−i-1-1110000i−i1-1−ii0000
χ2433-3-333-3-313-13-3-311-1-1−3i3i010-100-11−iii−i1-1−i−iii11-1-10000i−i-11i−i0000
χ25444444444-24-2-2-2-244-200-2-2-2-2-2-2000000000000000011110000000000
χ2644-4-444-4-4-4-24-2222-44-200-22-2-222000000000000000011-1-10000000000
χ274-44i−4i4-44i−4i040-44i−4i00000010-10i−i00000000000000001-1i−i000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ284-44i−4i4-44i−4i040-44i−4i00000010-10i−i00000000000000001-1i−i000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ294-44i−4i4-44i−4i040-44i−4i000000-2020−2i2i0000000000000000-22−2i2i0000000000
χ304-44i−4i4-44i−4i0-202−2i2i000000-2020−2i2i0000000000006−6i6−i61-1i−i0000000000
χ314-44i−4i4-44i−4i0-202−2i2i000000-2020−2i2i000000000000−66−i6i61-1i−i0000000000
χ324-4−4i4i4-4−4i4i040-4−4i4i00000010-10−ii00000000000000001-1−ii000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ334-4−4i4i4-4−4i4i040-4−4i4i00000010-10−ii00000000000000001-1−ii000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ344-4−4i4i4-4−4i4i040-4−4i4i000000-20202i−2i0000000000000000-222i−2i0000000000
χ354-4−4i4i4-4−4i4i0-2022i−2i000000-20202i−2i0000000000006−6−i6i61-1−ii0000000000
χ364-4−4i4i4-4−4i4i0-2022i−2i000000-20202i−2i000000000000−66i6−i61-1−ii0000000000
χ3766666666-2-3-2-3-3-31-2-2100010100220000-2-200001111000000-1-1000000
χ3866666666-2-3-2-3-3-31-2-2100010100-2-20000220000-1-1-1-100000011000000
χ396666-3-3-3-36060000-3-300000000000222200-1-1-1-1000000000000-1-10000
χ406666-3-3-3-36060000-3-300000000000-2-2-2-2001111000000000000110000
χ416666-3-3-3-3-20-20004114000-20-2000022-2-200-1-1-1-1000000000000110000
χ426666-3-3-3-3-20-20004114000-20-20000-2-222001111000000000000-1-10000
χ4366-6-666-6-62-3-2-333-12-21000-101002-20000-22000011-1-1000000-11000000
χ4466-6-666-6-62-3-2-333-12-21000-10100-2200002-20000-1-1110000001-1000000
χ4566-6-6-3-33320-2000-4-11400020-200002i−2i−2i2i00−i−iii000000000000i−i0000
χ4666-6-6-3-33320-2000-4-11400020-20000−2i2i2i−2i00ii−i−i000000000000−ii0000
χ4766-6-6-3-333-60600003-3000000000002i−2i2i−2i00−i−iii000000000000−ii0000
χ4866-6-6-3-333-60600003-300000000000−2i2i−2i2i00ii−i−i000000000000i−i0000
χ498-88i−8i8-88i−8i0-404−4i4i00000020-202i−2i0000000000000000-11−ii0000000000
χ508-8−8i8i8-8−8i8i0-4044i−4i00000020-20−2i2i0000000000000000-11i−i0000000000
χ5112121212-6-6-6-6-40-4000-422-400020200000000000000000000000000000000
χ521212-12-12-6-66640-40004-22-4000-20200000000000000000000000000000000
χ5312-1212i−12i-66−6i6i00000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000
χ5412-1212i−12i-66−6i6i00000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000
χ5512-12−12i12i-666i−6i00000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000
χ5612-12−12i12i-666i−6i00000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000

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