Finite Group Databasebeta

← Group #13180866

Character table — Group #13180866

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244446688881212121216161616161616161616161616161616181824243636363636363636363636363636363654547272727272727272
order1244336612121212361212243612126612123333666612121212121212122461222448888242424242424242424666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ3111111111111111111111111111111111111111111-1-1111-11-111-1-11111-1-1-1-1-1-11-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111-1-111-11-11-1-111-1-1-1-11111-1-1-11-1-1-11-1-1
χ511-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-111-1-111-11-111-1-111-1-1-111-111-11-1-1
χ611-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-111-1-11-11-1-111-1-111-11-11111-1-1-1
χ711-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1111-1-11-1-1111-1-1-1-1111-111-1-1-1-111
χ811-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-111-1-1-11111-1-11-1-1-1-1-11111
χ9222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000002200-1-100-1-1
χ10222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-200110011
χ1122222-12-122-1-1-1-1-1-12222222-12-12-1-1-12-1-1-122-1-1-1-1-1-100-1-1020200220000-1-1-1-1000-1000-100
χ1222222-12-122-1-1-1-1-1-12222222-12-12-1-1-12-1-1-122-1-1-1-1-1-100-1-10-20-200-2-2000011110001000100
χ132222-12-12-1-122-1-1-1-1222222-12-12-12-1-1-12-1-1-1-122-1-1-1-100-1-120202200-1-1-1-1000000-1000-1000
χ142222-12-12-1-122-1-1-1-1222222-12-12-12-1-1-12-1-1-1-122-1-1-1-100-1-1-20-20-2-200111100000010001000
χ1522-2-22222-2-2-2-222-2-2-22-1-111-2-222-1-1-1-1-1-1-1-1111111112-2-220000000000000000-2200-1-10011
χ1622-2-22222-2-2-2-222-2-2-22-1-111-2-222-1-1-1-1-1-1-1-111111111-22-2200000000000000002-2001100-1-1
χ1722-2-22-12-1-2-211-1-111-2222-2-2-212-12-1-1-12-1-1-1-2-2111111001-1020-200-22000011-1-1000-1000100
χ1822-2-22-12-1-2-211-1-111-2222-2-2-212-12-1-1-12-1-1-1-2-2111111001-10-202002-20000-1-1110001000-100
χ1922-2-2-12-1211-2-2-1-111-2222-2-21-2-12-12-1-1-12-1-111-2-21111001-120-202-200-1-111000000-10001000
χ2022-2-2-12-1211-2-2-1-111-2222-2-21-2-12-12-1-1-12-1-111-2-21111001-1-2020-220011-1-10000001000-1000
χ213333333333333333-1-10000-1-1-1-1000000000000000033-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111001100
χ223333333333333333-1-10000-1-1-1-1000000000000000033-1-1-1-1-1-1111111111111-1-1-1-100-1-100
χ233333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-11-11-1-1-111-1-1-1-11111111-1001-100
χ243333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-1-11-1111-1-11111-1-1-1-111-1100-1100
χ2533-3-33333-3-3-3-333-3-31-1000011-1-100000000000000003-31-11-1-11-11-11-1-111-1-1111-11-100-1100
χ2633-3-33333-3-3-3-333-3-31-1000011-1-100000000000000003-31-1-111-11-11-111-1-111-1-11-1-11001-100
χ2733-3-33333-3-3-3-333-3-31-1000011-1-10000000000000000-331-111-1-1-111-1-1-11111-1-1-111100-1-100
χ2833-3-33333-3-3-3-333-3-31-1000011-1-10000000000000000-331-1-1-1111-1-1111-1-1-1-111-11-1-1001100
χ2944444-24-244-2-2-2-2-2-244-2-2-2-24-24-2-2111-2111-2-211111100-2-200000000000000000000000000
χ304444-24-24-2-244-2-2-2-244-2-2-2-2-24-241-2111-21111-2-2111100-2-200000000000000000000000000
χ314444-2-2-2-2-2-2-2-21111444444-2-2-2-2-2-211-2-211-2-2-2-21111001100000000000000000000000000
χ324444-2-2-2-2-2-2-2-2111144-2-2-2-2-2-2-2-211−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i32001100000000000000000000000000
χ334444-2-2-2-2-2-2-2-2111144-2-2-2-2-2-2-2-211−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i32001100000000000000000000000000
χ3444-4-44-24-2-4-422-2-222-44-2-222-424-2-2111-211122-1-1-1-1-1-1002-200000000000000000000000000
χ3544-4-4-24-2422-4-4-2-222-44-2-2222-4-241-2111-211-1-122-1-1-1-1002-200000000000000000000000000
χ3644-4-4-2-2-2-2222211-1-1-4444-4-422-2-2-2-211-2-2112222-1-1-1-100-1100000000000000000000000000
χ3744-4-4-2-2-2-2222211-1-1-44-2-22222-2-211−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321+3i321−3i321−3i3200-1100000000000000000000000000
χ3844-4-4-2-2-2-2222211-1-1-44-2-22222-2-211−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321−3i321+3i321+3i3200-1100000000000000000000000000
χ394-44i−4i44-4-44i−4i4i−4i4-44i−4i001-1i−i00001111-1-1-1-1i−ii−ii−ii−i000000000000000000000000−i3i3003−3
χ404-44i−4i44-4-44i−4i4i−4i4-44i−4i001-1i−i00001111-1-1-1-1i−ii−ii−ii−i000000000000000000000000i3−i300−33
χ414-44i−4i44-4-44i−4i4i−4i4-44i−4i00-22−2i2i0000-2-2-2-22222−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ424-44i−4i4-2-424i−4i−2i2i-22−2i2i00-22−2i2i0000-21112-1-1-1−2i2ii−ii−ii−i0000000000000000i6−i66−60000000000
χ434-44i−4i4-2-424i−4i−2i2i-22−2i2i00-22−2i2i0000-21112-1-1-1−2i2ii−ii−ii−i0000000000000000−i6i6−660000000000
χ444-44i−4i-242-4−2i2i4i−4i-22−2i2i00-22−2i2i00001-211-12-1-1i−i−2i2ii−ii−i0000000000006−6i6−i600000000000000
χ454-44i−4i-242-4−2i2i4i−4i-22−2i2i00-22−2i2i00001-211-12-1-1i−i−2i2ii−ii−i000000000000−66−i6i600000000000000
χ464-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i001-1−ii00001111-1-1-1-1−ii−ii−ii−ii000000000000000000000000−i3i300−33
χ474-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i001-1−ii00001111-1-1-1-1−ii−ii−ii−ii000000000000000000000000i3−i3003−3
χ484-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i00-222i−2i0000-2-2-2-222222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ494-4−4i4i4-2-42−4i4i2i−2i-222i−2i00-222i−2i0000-21112-1-1-12i−2i−ii−ii−ii0000000000000000i6−i6−660000000000
χ504-4−4i4i4-2-42−4i4i2i−2i-222i−2i00-222i−2i0000-21112-1-1-12i−2i−ii−ii−ii0000000000000000−i6i66−60000000000
χ514-4−4i4i-242-42i−2i−4i4i-222i−2i00-222i−2i00001-211-12-1-1−ii2i−2i−ii−ii0000000000006−6−i6i600000000000000
χ524-4−4i4i-242-42i−2i−4i4i-222i−2i00-222i−2i00001-211-12-1-1−ii2i−2i−ii−ii000000000000−66i6−i600000000000000
χ5366666-36-366-3-3-3-3-3-3-2-20000-21-2100000000000000000011020200-2-200001111000-1000-100
χ5466666-36-366-3-3-3-3-3-3-2-20000-21-21000000000000000000110-20-200220000-1-1-1-10001000100
χ556666-36-36-3-366-3-3-3-3-2-200001-21-2000000000000000000112020-2-2001111000000-1000-1000
χ566666-36-36-3-366-3-3-3-3-2-200001-21-200000000000000000011-20-202200-1-1-1-100000010001000
χ5766-6-66-36-3-6-633-3-3332-200002-1-21000000000000000000-11020-2002-20000-1-111000-1000100
χ5866-6-66-36-3-6-633-3-3332-200002-1-21000000000000000000-110-20200-22000011-1-10001000-100
χ5966-6-6-36-3633-6-6-3-3332-20000-121-2000000000000000000-1120-20-220011-1-1000000-10001000
χ6066-6-6-36-3633-6-6-3-3332-20000-121-2000000000000000000-11-20202-200-1-1110000001000-1000
χ618-88i−8i8-4-848i−8i−4i4i-44−4i4i002-22i−2i00002-1-1-1-21112i−2i−ii−ii−ii000000000000000000000000000000
χ628-88i−8i-484-8−4i4i8i−8i-44−4i4i002-22i−2i0000-12-1-11-211−ii2i−2i−ii−ii000000000000000000000000000000
χ638-88i−8i-4-444−4i4i−4i4i2-22i−2i002-22i−2i0000-1-11−3i321+3i3211−1+3i32−1−3i32−ii−ii−2ζ14+ζ222ζ14−ζ22ζ14−2ζ22−ζ14+2ζ22000000000000000000000000000000
χ648-88i−8i-4-444−4i4i−4i4i2-22i−2i002-22i−2i0000-1-11+3i321−3i3211−1−3i32−1+3i32−ii−iiζ14−2ζ22−ζ14+2ζ22−2ζ14+ζ222ζ14−ζ22000000000000000000000000000000
χ658-88i−8i-4-444−4i4i−4i4i2-22i−2i00-44−4i4i000022-1-1-2-2112i−2i2i−2i−ii−ii000000000000000000000000000000
χ668-8−8i8i8-4-84−8i8i4i−4i-444i−4i002-2−2i2i00002-1-1-1-2111−2i2ii−ii−ii−i000000000000000000000000000000
χ678-8−8i8i-484-84i−4i−8i8i-444i−4i002-2−2i2i0000-12-1-11-211i−i−2i2ii−ii−i000000000000000000000000000000
χ688-8−8i8i-4-4444i−4i4i−4i2-2−2i2i002-2−2i2i0000-1-11−3i321+3i3211−1+3i32−1−3i32i−ii−i2ζ14−ζ22−2ζ14+ζ22−ζ14+2ζ22ζ14−2ζ22000000000000000000000000000000
χ698-8−8i8i-4-4444i−4i4i−4i2-2−2i2i002-2−2i2i0000-1-11+3i321−3i3211−1−3i32−1+3i32i−ii−i−ζ14+2ζ22ζ14−2ζ222ζ14−ζ22−2ζ14+ζ22000000000000000000000000000000
χ708-8−8i8i-4-4444i−4i4i−4i2-2−2i2i00-444i−4i000022-1-1-2-211−2i2i−2i2ii−ii−i000000000000000000000000000000
χ7112121212-6-6-6-6-6-6-6-63333-4-400002222000000000000000000-1-100000000000000000000000000
χ721212-12-12-6-6-6-6666633-3-34-40000-2-2220000000000000000001-100000000000000000000000000

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