Finite Group Databasebeta

← Group #13166106

Character table — Group #13166106

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244446688881212121216161616161616161616161616161616181824243636363636363636363636363636363654547272727272727272
order124433661212121236121224361212661212333366661212121212121212246124444888812121212121212122466121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ511-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11i−ii−ii−ii−iii−i−iii−i−i-1111-1-1i−ii−i
χ611-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11−ii−ii−ii−ii−i−iii−i−iii-1111-1-1−ii−ii
χ711-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11i−i−iii−i−iiii−i−i−i−iii1-1-1-111i−i−ii
χ811-1-11111-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11−iii−i−iii−i−i−iiiii−i−i1-1-1-111−iii−i
χ9222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022-1-1-1-10000
χ10222222222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-211110000
χ1122222-12-122-1-1-1-1-1-12222222-12-12-1-1-12-1-1-122-1-1-1-1-1-100-1-1002200220000-1-1-1-100000000-1-1
χ1222222-12-122-1-1-1-1-1-12222222-12-12-1-1-12-1-1-122-1-1-1-1-1-100-1-100-2-200-2-2000011110000000011
χ132222-12-12-1-122-1-1-1-1222222-12-12-12-1-1-12-1-1-1-122-1-1-1-100-1-122002200-1-1-1-10000000000-1-100
χ142222-12-12-1-122-1-1-1-1222222-12-12-12-1-1-12-1-1-1-122-1-1-1-100-1-1-2-200-2-200111100000000001100
χ1522-2-22222-2-2-2-222-2-2-22-1-111-2-222-1-1-1-1-1-1-1-1111111112-2-220000000000000000-22-1-1110000
χ1622-2-22222-2-2-2-222-2-2-22-1-111-2-222-1-1-1-1-1-1-1-111111111-22-2200000000000000002-211-1-10000
χ1722-2-22-12-1-2-211-1-111-2222-2-2-212-12-1-1-12-1-1-1-2-2111111001-1002i−2i002i−2i0000−i−iii00000000−ii
χ1822-2-22-12-1-2-211-1-111-2222-2-2-212-12-1-1-12-1-1-1-2-2111111001-100−2i2i00−2i2i0000ii−i−i00000000i−i
χ1922-2-2-12-1211-2-2-1-111-2222-2-21-2-12-12-1-1-12-1-111-2-21111001-12i−2i002i−2i00−i−iii0000000000−ii00
χ2022-2-2-12-1211-2-2-1-111-2222-2-21-2-12-12-1-1-12-1-111-2-21111001-1−2i2i00−2i2i00ii−i−i0000000000i−i00
χ213333333333333333-1-10000-1-1-1-1000000000000000033-1-11111-1-1-1-111111111-1-10000-1-1-1-1
χ223333333333333333-1-10000-1-1-1-1000000000000000033-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-100001111
χ233333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-111-1-1-1-1111111-1-1-1-1110000-1-111
χ243333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-1-1-11111-1-1-1-1-1-1111111000011-1-1
χ2533-3-33333-3-3-3-333-3-31-1000011-1-100000000000000003-31-1i−ii−i−ii−iiii−i−iii−i−i1-10000−ii−ii
χ2633-3-33333-3-3-3-333-3-31-1000011-1-100000000000000003-31-1−ii−iii−ii−i−i−iii−i−iii1-10000i−ii−i
χ2733-3-33333-3-3-3-333-3-31-1000011-1-10000000000000000-331-1i−i−ii−iii−iii−i−i−i−iii-110000−iii−i
χ2833-3-33333-3-3-3-333-3-31-1000011-1-10000000000000000-331-1−iii−ii−i−ii−i−iiiii−i−i-110000i−i−ii
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−i0000000000000000000000−i3i33−30000
χ404-44i−4i44-4-44i−4i4i−4i4-44i−4i001-1i−i00001111-1-1-1-1i−ii−ii−ii−i0000000000000000000000i3−i3−330000
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−i0000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000
χ434-44i−4i4-2-424i−4i−2i2i-22−2i2i00-22−2i2i0000-21112-1-1-1−2i2ii−ii−ii−i0000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000
χ444-44i−4i-242-4−2i2i4i−4i-22−2i2i00-22−2i2i00001-211-12-1-1i−i−2i2ii−ii−i000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000
χ454-44i−4i-242-4−2i2i4i−4i-22−2i2i00-22−2i2i00001-211-12-1-1i−i−2i2ii−ii−i000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000
χ464-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i001-1−ii00001111-1-1-1-1−ii−ii−ii−ii0000000000000000000000−i3i3−330000
χ474-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i001-1−ii00001111-1-1-1-1−ii−ii−ii−ii0000000000000000000000i3−i33−30000
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−ii0000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000
χ504-4−4i4i4-2-42−4i4i2i−2i-222i−2i00-222i−2i0000-21112-1-1-12i−2i−ii−ii−ii0000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000
χ514-4−4i4i-242-42i−2i−4i4i-222i−2i00-222i−2i00001-211-12-1-1−ii2i−2i−ii−ii000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000
χ524-4−4i4i-242-42i−2i−4i4i-222i−2i00-222i−2i00001-211-12-1-1−ii2i−2i−ii−ii000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000
χ5366666-36-366-3-3-3-3-3-3-2-20000-21-2100000000000000000011002200-2-20000-1-1-1-10000000011
χ5466666-36-366-3-3-3-3-3-3-2-20000-21-210000000000000000001100-2-200220000111100000000-1-1
χ556666-36-36-3-366-3-3-3-3-2-200001-21-2000000000000000000112200-2-200-1-1-1-100000000001100
χ566666-36-36-3-366-3-3-3-3-2-200001-21-200000000000000000011-2-200220011110000000000-1-100
χ5766-6-66-36-3-6-633-3-3332-200002-1-21000000000000000000-11002i−2i00−2i2i0000−i−iii00000000i−i
χ5866-6-66-36-3-6-633-3-3332-200002-1-21000000000000000000-1100−2i2i002i−2i0000ii−i−i00000000−ii
χ5966-6-6-36-3633-6-6-3-3332-20000-121-2000000000000000000-112i−2i00−2i2i00−i−iii0000000000i−i00
χ6066-6-6-36-3633-6-6-3-3332-20000-121-2000000000000000000-11−2i2i002i−2i00ii−i−i0000000000−ii00
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−2ζ7+ζ112ζ7−ζ11ζ7−2ζ11−ζ7+2ζ11000000000000000000000000000000
χ648-88i−8i-4-444−4i4i−4i4i2-22i−2i002-22i−2i0000-1-11+3i321−3i3211−1−3i32−1+3i32−ii−iiζ7−2ζ11−ζ7+2ζ11−2ζ7+ζ112ζ7−ζ11000000000000000000000000000000
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−i2ζ7−ζ11−2ζ7+ζ11−ζ7+2ζ11ζ7−2ζ11000000000000000000000000000000
χ698-8−8i8i-4-4444i−4i4i−4i2-2−2i2i002-2−2i2i0000-1-11+3i321−3i3211−1−3i32−1+3i32i−ii−i−ζ7+2ζ11ζ7−2ζ112ζ7−ζ11−2ζ7+ζ11000000000000000000000000000000
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 12 (ζ12 = 1); i = ζ3.