Finite Group Databasebeta

← Group #13180878

Character table — Group #13180878

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1122222223344444666666688121212121216161616161616161616161616161616161818181818183636363636363636363636363636545472727272144144
order12233666622366662666666366666633336666666666666222444224444666612121212246121212612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1111-1-1-11-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-1-1-1-11111-1-1
χ511-1111-1-11111-11-1-1-11-1-111111-111-1-11111-11111-1-1-1-1-1-1-1-1111-111-11-1-1-1111-1-111-1-11-11-11-11-1
χ611-1111-1-11111-11-1-1-11-1-111111-111-1-11111-11111-1-1-1-1-1-1-1-111-1111-1-111-1-111-1-111-1-1-11-11-11-11
χ711-1111-1-11111-11-1-1-11-1-111111-111-1-11111-11111-1-1-1-1-1-1-1-1-1-11-1-1-11-1111-1-1-111-1-1111-1-11-111-1
χ811-1111-1-11111-11-1-1-11-1-111111-111-1-11111-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-111-1-111-111-11-1-11
χ922222222222222222222222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100220000000000000000220000-1-1
χ1022222222222222222222222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2000011
χ112222-1-1-1-1222-12-1-1-12-1-1-122-1222-1-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1220022200020-1-1-1-1-1-1-1-100000000
χ122222-1-1-1-1222-12-1-1-12-1-1-122-1222-1-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1-2-200-2-2-2000-201111111100000000
χ13222-12222-122-1-1-1-1-12222-1-1222-1-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-10000000222020000000000-1-1-1-100
χ14222-12222-122-1-1-1-1-12222-1-1222-1-1-1-1-1-12-1-12-12-1-1-1-122-1-1-1-10000000-2-2-20-20000000000111100
χ1522-2222-2-22222-22-2-2-22-2-2222-1-1-222-2-2-1-1-1-11-1-1-1-111111111002-200000000000000002-20000-11
χ1622-2222-2-22222-22-2-2-22-2-2222-1-1-222-2-2-1-1-1-11-1-1-1-11111111100-220000000000000000-2200001-1
χ1722-22-1-111222-1-2-111-2-11122-122-2-1-1112-1-1-1-22-1-1-1-2-2111111220022-2000-20-1-111-1-11100000000
χ1822-22-1-111222-1-2-111-2-11122-122-2-1-1112-1-1-1-22-1-1-1-2-2111111-2-200-2-220002011-1-111-1-100000000
χ1922-2-122-2-2-122-11-111-22-2-2-1-12221-1-111-12-1-1-2-12-1-111-2-2111100000002-2-2020000000000-11-1100
χ2022-2-122-2-2-122-11-111-22-2-2-1-12221-1-111-12-1-1-2-12-1-111-2-211110000000-2220-200000000001-11-100
χ212-2022-200-2-2220-2000-2002-222-202-20022220-2-2-2-2000000002-2002-20000002-2002-20000000000
χ222-2022-200-2-2220-2000-2002-222-202-20022220-2-2-2-200000000-2200-22000000-2200-220000000000
χ232-202-11i3−i3-2-22-101i3−i301i3−i32-2-12-20-11i3−i32-1-1-10-211100i3−i3i3i3−i3−i32-2002-2000000-11i3−i3-11i3−i300000000
χ242-202-11i3−i3-2-22-101i3−i301i3−i32-2-12-20-11i3−i32-1-1-10-211100i3−i3i3i3−i3−i3-2200-220000001-1−i3i31-1−i3i300000000
χ252-202-11−i3i3-2-22-101−i3i301−i3i32-2-12-20-11−i3i32-1-1-10-211100−i3i3−i3−i3i3i32-2002-2000000-11−i3i3-11−i3i300000000
χ262-202-11−i3i3-2-22-101−i3i301−i3i32-2-12-20-11−i3i32-1-1-10-211100−i3i3−i3−i3i3i3-2200-220000001-1i3−i31-1i3−i300000000
χ27333333333-1-133333-1-1-1-1-1-1-100-1-1-1-1-1000000000000000001133-1-1111-1-1-11111-1-1-1-1-1-111-1-100
χ28333333333-1-133333-1-1-1-1-1-1-100-1-1-1-1-10000000000000000011-3-3-1-11-1-11-111111-1-1-1-111-1-11100
χ29333333333-1-133333-1-1-1-1-1-1-100-1-1-1-1-100000000000000000-1-13311-1-1-1111-1-1-1-11111-1-1-1-11100
χ30333333333-1-133333-1-1-1-1-1-1-100-1-1-1-1-100000000000000000-1-1-3-311-111-11-1-1-1-1-111111111-1-100
χ3133-3333-3-33-1-13-33-3-31-111-1-1-1001-1-11100000000000000000113-3-1-1-11-111-111-1-1-1-111-111-1-1100
χ3233-3333-3-33-1-13-33-3-31-111-1-1-1001-1-1110000000000000000011-33-1-1-1-11-11111-1-1-1-1111-1-111-100
χ3333-3333-3-33-1-13-33-3-31-111-1-1-1001-1-11100000000000000000-1-13-3111-11-1-11-1-11111-1-1-11-111-100
χ3433-3333-3-33-1-13-33-3-31-111-1-1-1001-1-11100000000000000000-1-1-331111-11-1-1-1-11111-1-11-11-1-1100
χ354444-2-2-2-2444-24-2-2-24-2-2-244-2-2-24-2-2-2-2-2111-2-2111-2-21111110000000000000000000000000000
χ36444-24444-244-2-2-2-2-24444-2-24-2-2-2-2-2-2-21-211-21-21111-2-211110000000000000000000000000000
χ37444-2-2-2-2-2-2441-21114-2-2-2-2-2-244-21111-2-2114-2-211-2-2-2-211110000000000000000000000000000
χ38444-2-2-2-2-2-2441-21114-2-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32-211−1+3i32−1−3i321111−1+3i32−1−3i32−1+3i32−1−3i320000000000000000000000000000
χ39444-2-2-2-2-2-2441-21114-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32-211−1−3i32−1+3i321111−1−3i32−1+3i32−1−3i32−1+3i320000000000000000000000000000
χ4044-44-2-222444-2-4-222-4-22244-2-2-2-4-2-222-21112-211122-1-1-1-1-1-10000000000000000000000000000
χ4144-4-244-4-4-244-22-222-44-4-4-2-24-2-22-2-2221-21121-211-1-122-1-1-1-10000000000000000000000000000
χ4244-4-2-2-222-244121-1-1-4-222-2-2-244211-1-1-2-211-4-2-2112222-1-1-1-10000000000000000000000000000
χ4344-4-2-2-222-244121-1-1-4-222-2-2-2-2-2211-1-111−1+3i32−1−3i32211−1+3i32−1−3i32-1-1-1-11−3i321+3i321−3i321+3i320000000000000000000000000000
χ4444-4-2-2-222-244121-1-1-4-222-2-2-2-2-2211-1-111−1−3i32−1+3i32211−1−3i32−1+3i32-1-1-1-11+3i321−3i321+3i321−3i320000000000000000000000000000
χ454-4044-400-4-4440-4000-4004-44-2204-400-2-2-2-202222000000000000000000000000000000000000
χ464-404-222i3−2i3-4-44-2022i3−2i3022i3−2i34-4-2-220-222i3−2i3-211102-1-1-100−i3i3−i3−i3i3i30000000000000000000000000000
χ474-404-22−2i32i3-4-44-202−2i32i302−2i32i34-4-2-220-22−2i32i3-211102-1-1-100i3−i3i3i3−i3−i30000000000000000000000000000
χ484-40-24-4002-44-202000-400-2244-40-2200-24-2-202-422000000000000000000000000000000000000
χ494-40-24-4002-44-202000-400-224-220-22001-2110-12-1-13-3003-3-330000000000000000000000000000
χ504-40-24-4002-44-202000-400-224-220-22001-2110-12-1-1-3300-333-30000000000000000000000000000
χ514-40-2-222i3−2i32-4410-1−i3i3022i3−2i3-22-24-401-1−i3i3-2-211022-1-1002i3−2i3−i3−i3i3i30000000000000000000000000000
χ524-40-2-222i3−2i32-4410-1−i3i3022i3−2i3-22-2-2201-1−i3i311−1+3i32−1−3i320-1-11−3i321+3i323-3−i3i3−3+i323+i323−i32−3−i320000000000000000000000000000
χ534-40-2-222i3−2i32-4410-1−i3i3022i3−2i3-22-2-2201-1−i3i311−1−3i32−1+3i320-1-11+3i321−3i32-33−i3i33+i32−3+i32−3−i323−i320000000000000000000000000000
χ544-40-2-22−2i32i32-4410-1i3−i302−2i32i3-22-24-401-1i3−i3-2-211022-1-100−2i32i3i3i3−i3−i30000000000000000000000000000
χ554-40-2-22−2i32i32-4410-1i3−i302−2i32i3-22-2-2201-1i3−i311−1+3i32−1−3i320-1-11−3i321+3i32-33i3−i33−i32−3−i32−3+i323+i320000000000000000000000000000
χ564-40-2-22−2i32i32-4410-1i3−i302−2i32i3-22-2-2201-1i3−i311−1−3i32−1+3i320-1-11+3i321−3i323-3i3−i3−3−i323−i323+i32−3+i320000000000000000000000000000
χ576666-3-3-3-36-2-2-36-3-3-3-2111-2-2100-21111000000000000000002200-2-22000-20-1-1-1-1111100000000
χ586666-3-3-3-36-2-2-36-3-3-3-2111-2-2100-2111100000000000000000-2-20022-2000201111-1-1-1-100000000
χ59666-36666-3-2-2-3-3-3-3-3-2-2-2-211-2001111100000000000000000000000022-20-20000000000-1-11100
χ60666-36666-3-2-2-3-3-3-3-3-2-2-2-211-20011111000000000000000000000000-2-2202000000000011-1-100
χ6166-66-3-3336-2-2-3-6-33321-1-1-2-2100211-1-1000000000000000002200-2-2-200020-1-11111-1-100000000
χ6266-66-3-3336-2-2-3-6-33321-1-1-2-2100211-1-100000000000000000-2-200222000-2011-1-1-1-11100000000
χ6366-6-366-6-6-3-2-2-33-3332-22211-200-111-1-10000000000000000000000002-220-20000000000-111-100
χ6466-6-366-6-6-3-2-2-33-3332-22211-200-111-1-1000000000000000000000000-22-20200000000001-1-1100
χ656-6066-600-62-260-6000200-22-2000-2200000000000000000002-200-220000002-200-220000000000
χ666-6066-600-62-260-6000200-22-2000-220000000000000000000-22002-2000000-22002-20000000000
χ676-606-333i3−3i3-62-2-3033i3−3i30-1−i3i3-2210001-1−i3i3000000000000000002-200-22000000-11i3−i31-1−i3i300000000
χ686-606-333i3−3i3-62-2-3033i3−3i30-1−i3i3-2210001-1−i3i300000000000000000-22002-20000001-1−i3i3-11i3−i300000000
χ696-606-33−3i33i3-62-2-303−3i33i30-1i3−i3-2210001-1i3−i3000000000000000002-200-22000000-11−i3i31-1i3−i300000000
χ706-606-33−3i33i3-62-2-303−3i33i30-1i3−i3-2210001-1i3−i300000000000000000-22002-20000001-1i3−i3-11−i3i300000000
χ71121212-6-6-6-6-6-6-4-43-6333-4222222002-1-1-1-1000000000000000000000000000000000000000000000
χ721212-12-6-6-666-6-4-4363-3-342-2-222200-2-1-111000000000000000000000000000000000000000000000
χ7312-120-612-120064-4-6060004002-2-40002-200000000000000000000000000000000000000000000000
χ7412-120-6-666i3−6i364-430-3−3i33i30-2−2i32i32-22000-11i3−i3000000000000000000000000000000000000000000000
χ7512-120-6-66−6i36i364-430-33i3−3i30-22i3−2i32-22000-11−i3i3000000000000000000000000000000000000000000000

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