Finite Group Databasebeta

← Group #13166094

Character table — Group #13166094

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244446688881212121216161616161616161616161616161616181824243636363636363636363636363636363654547272727272727272
order122233666666366644366612121212333366666666666622121244448888242424242424242444666612121212
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
χ51-1-1111-1-111-1-11-1-111-111-1-111-1-111111111-1-1-1-1-1-1-1-11-11-1i−ii−ii−ii−iii−i−iii−i−i1-111-1-1i−ii−i
χ61-1-1111-1-111-1-11-1-111-111-1-111-1-111111111-1-1-1-1-1-1-1-11-11-1−ii−ii−ii−ii−i−iii−i−iii1-111-1-1−ii−ii
χ71-1-1111-1-111-1-11-1-111-111-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1i−i−iii−i−iiii−i−i−i−iii-11-1-111i−i−ii
χ81-1-1111-1-111-1-11-1-111-111-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1−iii−i−iii−i−i−iiiii−i−i-11-1-111−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
χ1122222-12-12-12-1-1-1-1-12222222-12-12-1-1-12-1-1-122-1-1-1-1-1-100-1-1002200220000-1-1-1-100000000-1-1
χ1222222-12-12-12-1-1-1-1-12222222-12-12-1-1-12-1-1-122-1-1-1-1-1-100-1-100-2-200-2-2000011110000000011
χ132222-12-12-12-12-1-1-1-1222222-12-12-12-1-1-12-1-1-1-122-1-1-1-100-1-122002200-1-1-1-10000000000-1-100
χ142222-12-12-12-12-1-1-1-1222222-12-12-12-1-1-12-1-1-1-122-1-1-1-100-1-1-2-200-2-200111100000000001100
χ152-2-2222-2-222-2-22-2-222-2-1-11122-2-2-1-1-1-1-1-1-1-1111111112-22-200000000000000002-2-1-1110000
χ162-2-2222-2-222-2-22-2-222-2-1-11122-2-2-1-1-1-1-1-1-1-111111111-222-20000000000000000-2211-1-10000
χ172-2-222-1-212-1-21-111-12-222-2-22-1-212-1-1-12-1-1-1-2-211111100-11002i−2i002i−2i0000−i−iii00000000−ii
χ182-2-222-1-212-1-21-111-12-222-2-22-1-212-1-1-12-1-1-1-2-211111100-1100−2i2i00−2i2i0000ii−i−i00000000i−i
χ192-2-22-121-2-121-2-111-12-222-2-2-121-2-12-1-1-12-1-111-2-2111100-112i−2i002i−2i00−i−iii0000000000−ii00
χ202-2-22-121-2-121-2-111-12-222-2-2-121-2-12-1-1-12-1-111-2-2111100-11−2i2i00−2i2i00ii−i−i0000000000i−i00
χ213333333333333333-1-10000-1-1-1-1000000000000000033-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111
χ223333333333333333-1-10000-1-1-1-1000000000000000033-1-1-1-1-1-1111111111111-1-10000-1-1-1-1
χ233333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-111-1-1-1-111-1-1-1-1111111000011-1-1
χ243333333333333333-1-10000-1-1-1-10000000000000000-3-3-1-1-1-11111-1-11111-1-1-1-1110000-1-111
χ253-3-3333-3-333-3-33-3-33-110000-1-11100000000000000003-3-11i−ii−i−ii−ii−i−iii−i−iii-110000i−ii−i
χ263-3-3333-3-333-3-33-3-33-110000-1-11100000000000000003-3-11−ii−iii−ii−iii−i−iii−i−i-110000−ii−ii
χ273-3-3333-3-333-3-33-3-33-110000-1-1110000000000000000-33-11i−i−ii−iii−i−i−iiiii−i−i1-10000i−i−ii
χ283-3-3333-3-333-3-33-3-33-110000-1-1110000000000000000-33-11−iii−ii−i−iiii−i−i−i−iii1-10000−iii−i
χ2944444-24-24-24-2-2-2-2-244-2-2-2-24-24-2-2111-2111-2-211111100-2-200000000000000000000000000
χ304444-24-24-24-24-2-2-2-244-2-2-2-2-24-241-2111-21111-2-2111100-2-200000000000000000000000000
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
χ3444-4-4444-4-4-4-4444-4-4001-11-100001111-1-1-1-11-11-11-11-10000000000000000000000−i3i3−i3i30000
χ3544-4-4444-4-4-4-4444-4-4001-11-100001111-1-1-1-11-11-11-11-10000000000000000000000i3−i3i3−i30000
χ3644-4-4444-4-4-4-4444-4-400-22-220000-2-2-2-22222-22-22-22-22000000000000000000000000000000
χ3744-4-44-242-42-4-2-2-22200-22-220000-21112-1-1-1-221-11-11-100000000000000006−66−60000000000
χ3844-4-44-242-42-4-2-2-22200-22-220000-21112-1-1-1-221-11-11-10000000000000000−66−660000000000
χ3944-4-4-24-2-42-424-2-22200-22-2200001-211-12-1-11-1-221-11-1000000000000i6−i6i6−i600000000000000
χ4044-4-4-24-2-42-424-2-22200-22-2200001-211-12-1-11-1-221-11-1000000000000−i6i6−i6i600000000000000
χ414-44-444-44-4-44-44-44-4001-1-1100001111-1-1-1-1-11-11-11-110000000000000000000000−i3i3i3−i30000
χ424-44-444-44-4-44-44-44-4001-1-1100001111-1-1-1-1-11-11-11-110000000000000000000000i3−i3−i3i30000
χ434-44-444-44-4-44-44-44-400-222-20000-2-2-2-222222-22-22-22-2000000000000000000000000000000
χ444-44-44-2-4-2-4242-22-2200-222-20000-21112-1-1-12-2-11-11-110000000000000000i6−i6−i6i60000000000
χ454-44-44-2-4-2-4242-22-2200-222-20000-21112-1-1-12-2-11-11-110000000000000000−i6i6i6−i60000000000
χ464-44-4-24242-4-2-4-22-2200-222-200001-211-12-1-1-112-2-11-110000000000006−6−6600000000000000
χ474-44-4-24242-4-2-4-22-2200-222-200001-211-12-1-1-112-2-11-11000000000000−666−600000000000000
χ484-4-444-2-424-2-42-222-24-4-2-2224-2-42-2111-211122-1-1-1-1-1-100-2200000000000000000000000000
χ494-4-44-242-4-242-4-222-24-4-2-222-242-41-2111-211-1-122-1-1-1-100-2200000000000000000000000000
χ504-4-44-2-222-2-2221-1-114-444-4-4-2-222-2-211-2-2112222-1-1-1-1001-100000000000000000000000000
χ514-4-44-2-222-2-2221-1-114-4-2-222-2-22211−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321+3i321−3i321−3i32001-100000000000000000000000000
χ524-4-44-2-222-2-2221-1-114-4-2-222-2-22211−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321−3i321+3i321+3i32001-100000000000000000000000000
χ5366666-36-36-36-3-3-3-3-3-2-20000-21-2100000000000000000011002200-2-20000111100000000-1-1
χ5466666-36-36-36-3-3-3-3-3-2-20000-21-210000000000000000001100-2-200220000-1-1-1-10000000011
χ556666-36-36-36-36-3-3-3-3-2-200001-21-2000000000000000000112200-2-20011110000000000-1-100
χ566666-36-36-36-36-3-3-3-3-2-200001-21-200000000000000000011-2-2002200-1-1-1-100000000001100
χ576-6-666-3-636-3-63-333-3-220000-212-10000000000000000001-1002i−2i00−2i2i0000ii−i−i00000000−ii
χ586-6-666-3-636-3-63-333-3-220000-212-10000000000000000001-100−2i2i002i−2i0000−i−iii00000000i−i
χ596-6-66-363-6-363-6-333-3-2200001-2-120000000000000000001-12i−2i00−2i2i00ii−i−i0000000000−ii00
χ606-6-66-363-6-363-6-333-3-2200001-2-120000000000000000001-1−2i2i002i−2i00−i−iii0000000000i−i00
χ6188-8-88-484-84-8-4-4-444002-22-200002-1-1-1-21112-2-11-11-11000000000000000000000000000000
χ6288-8-8-48-4-84-848-4-444002-22-20000-12-1-11-211-112-2-11-11000000000000000000000000000000
χ6388-8-8-4-4-44444-422-2-2002-22-20000-1-11−3i321+3i3211−1+3i32−1−3i32-11-111−3i32−1+3i321+3i32−1−3i32000000000000000000000000000000
χ6488-8-8-4-4-44444-422-2-2002-22-20000-1-11+3i321−3i3211−1−3i32−1+3i32-11-111+3i32−1−3i321−3i32−1+3i32000000000000000000000000000000
χ6588-8-8-4-4-44444-422-2-200-44-44000022-1-1-2-2112-22-2-11-11000000000000000000000000000000
χ668-88-88-4-8-4-8484-44-44002-2-2200002-1-1-1-2111-221-11-11-1000000000000000000000000000000
χ678-88-8-48484-8-4-8-44-44002-2-220000-12-1-11-2111-1-221-11-1000000000000000000000000000000
χ688-88-8-4-44-444-442-22-2002-2-220000-1-11−3i321+3i3211−1+3i32−1−3i321-11-1−1+3i321−3i32−1−3i321+3i32000000000000000000000000000000
χ698-88-8-4-44-444-442-22-2002-2-220000-1-11+3i321−3i3211−1−3i32−1+3i321-11-1−1−3i321+3i32−1+3i321−3i32000000000000000000000000000000
χ708-88-8-4-44-444-442-22-200-444-4000022-1-1-2-211-22-221-11-1000000000000000000000000000000
χ7112121212-6-6-6-6-6-6-6-63333-4-400002222000000000000000000-1-100000000000000000000000000
χ7212-12-1212-6-666-6-6663-3-33-44000022-2-2000000000000000000-1100000000000000000000000000

Here i is the imaginary unit (i² = −1).