Finite Group Databasebeta

← Group #13180824

Character table — Group #13180824

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222224444666666668888888888881212121216161616161616161616161618182424242424242424242424242424363636363636363636367272108108108108
order12443366121212123612122244661212333666121212121212661212333666121212121212246666666121212121212122468812242424246122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-11-1-1-1-11111111111111111111111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-111-111-1111111-1-1-1-1
χ411111111111111111-1-11-1-1-1-11111111111111111111111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511-1-11111-1-1-1-111-1-1-11-1111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-11111111-1-1-1-1-1-11-1-11-1111-1-11-1-111-1
χ611-1-11111-1-1-1-111-1-1-11-1111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1-11-1-111-1-111-111-1-11
χ711-1-11111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-111-1-111-1-11-11-1-11
χ811-1-11111-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111-111-11-1-1-111-11-111-1
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-12-1-1-1-1-1-10020020000000000
χ1022222222222222222-2-22-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-22111111211111100-200-20000000000
χ1122222-12-122-1-1-1-1-1-1200200002222222222222-12-1-1-1-1-1-1-1-1-1-1-1-1-100-1000000-1000000220220-1-1-1-1-1-10000
χ1222222-12-122-1-1-1-1-1-1200200002222222222222-12-1-1-1-1-1-1-1-1-1-1-1-1-100-1000000-1000000-2-20-2-201111110000
χ132222-12-12-1-122-1-1-1-12222-1-1-1-12-1-12-1-122-1-1-1-1-12-122-1-12-1-122-1-1-1-122-122-1-1-1-1-122-1-1-1-100-100-10000000000
χ142222-12-12-1-122-1-1-1-12222-1-1-1-1-12-1-12-1-1-122-1-1-12-12-12-1-12-1-1-122-1-122-1-1-122-1-1-1-1-122-1-100-100-10000000000
χ152222-12-12-1-122-1-1-1-12222-1-1-1-1-1-12-1-12-1-1-1-122-12-12-1-12-1-12-1-1-1-12222-1-1-1-1-122-1-1-1-1-12200-100-10000000000
χ162222-12-12-1-122-1-1-1-12-2-2211112-1-12-1-122-1-1-1-1-12-122-1-12-1-122-1-1-1-1-2-2-1-2-21111-1-2-211110010010000000000
χ172222-12-12-1-122-1-1-1-12-2-221111-12-1-12-1-1-122-1-1-12-12-12-1-12-1-1-122-1-1-2-2-111-2-211-111-2-2110010010000000000
χ182222-12-12-1-122-1-1-1-12-2-221111-1-12-1-12-1-1-1-122-12-12-1-12-1-12-1-1-1-122-2-2-11111-2-2-11111-2-20010010000000000
χ1922-2-22222-2-2-2-222-2-2-22-2222-2-2-1-1-1-1-1-1111111-2-222-1-1-1-1-1-1111111-22-2-1-1-1-1-1-1211111100-20020000000000
χ2022-2-22222-2-2-2-222-2-2-2-222-2-222-1-1-1-1-1-1111111-2-222-1-1-1-1-1-11111112-2-21111112-1-1-1-1-1-100200-20000000000
χ2122-2-22-12-1-2-211-1-111-20020000222222-2-2-2-2-2-2-212-1-1-1-1-1-1-1111111001000000-10000002-202-20-1-111-110000
χ2222-2-22-12-1-2-211-1-111-20020000222222-2-2-2-2-2-2-212-1-1-1-1-1-1-1111111001000000-1000000-220-22011-1-11-10000
χ2322-2-2-12-1211-2-2-1-111-22-22-1-1112-1-12-1-1-2-211111-2-122-1-12-1-1-2-21111-22122-1-1-1-1-1-2-2111100100-10000000000
χ2422-2-2-12-1211-2-2-1-111-22-22-1-111-12-1-12-111-2-2111-2-12-12-1-12-111-2-211-221-1-122-1-1-111-2-21100100-10000000000
χ2522-2-2-12-1211-2-2-1-111-22-22-1-111-1-12-1-121111-2-21-2-12-1-12-1-121111-2-2-221-1-1-1-122-11111-2-200100-10000000000
χ2622-2-2-12-1211-2-2-1-111-2-22211-1-12-1-12-1-1-2-211111-2-122-1-12-1-1-2-211112-21-2-21111-122-1-1-1-100-10010000000000
χ2722-2-2-12-1211-2-2-1-111-2-22211-1-1-12-1-12-111-2-2111-2-12-12-1-12-111-2-2112-2111-2-211-1-1-122-1-100-10010000000000
χ2822-2-2-12-1211-2-2-1-111-2-22211-1-1-1-12-1-121111-2-21-2-12-1-12-1-121111-2-22-211111-2-2-1-1-1-1-12200-10010000000000
χ293333333333333333-133-13333000000000000-1-1-1-1000000000000-1-1-1000000-100000011-1-1-1-1-1-1-1-11111-1-1
χ303333333333333333-133-13333000000000000-1-1-1-1000000000000-1-1-1000000-1000000-1-1-111-11111-1-1-1-111
χ313333333333333333-1-3-3-1-3-3-3-3000000000000-1-1-1-100000000000011-1000000-1000000111-1-11-1-1-1-111-1-111
χ323333333333333333-1-3-3-1-3-3-3-3000000000000-1-1-1-100000000000011-1000000-1000000-1-111111111-1-111-1-1
χ3333-3-33333-3-3-3-333-3-313-3-133-3-300000000000011-1-10000000000001-11000000-10000001-11-11-1-1-1111-1-11-11
χ3433-3-33333-3-3-3-333-3-313-3-133-3-300000000000011-1-10000000000001-11000000-1000000-1111-1-111-1-1-111-11-1
χ3533-3-33333-3-3-3-333-3-31-33-1-3-33300000000000011-1-1000000000000-111000000-10000001-1-1-111-1-1111-11-11-1
χ3633-3-33333-3-3-3-333-3-31-33-1-3-33300000000000011-1-1000000000000-111000000-1000000-11-11-1111-1-1-11-11-11
χ3744444-24-244-2-2-2-2-2-240040000-2-2-2-2-2-2-2-2-2-2-2-24-24-211111111111100-2000000-20000000000000000000000
χ384444-2-2-2-2-2-2-2-21111400400004-2-24-2-244-2-2-2-2-2-2-2-2-211-211-2-2111100100000010000000000000000000000
χ394444-2-2-2-2-2-2-2-2111140040000-24-2-24-2-2-244-2-2-2-2-2-21-211-2111-2-21100100000010000000000000000000000
χ404444-2-2-2-2-2-2-2-2111140040000-2-24-2-24-2-2-2-244-2-2-2-211-211-21111-2-200100000010000000000000000000000
χ4144-4-44-24-2-4-422-2-222-40040000-2-2-2-2-2-2222222-424-2111111-1-1-1-1-1-1002000000-20000000000000000000000
χ4244-4-4-2-2-2-2222211-1-1-400400004-2-24-2-2-4-4222222-2-2-211-21122-1-1-1-100-100000010000000000000000000000
χ4344-4-4-2-2-2-2222211-1-1-40040000-24-2-24-222-4-42222-2-21-211-21-1-122-1-100-100000010000000000000000000000
χ4444-4-4-2-2-2-2222211-1-1-40040000-2-24-2-242222-4-422-2-211-211-2-1-1-1-12200-100000010000000000000000000000
χ454-44i−4i44-4-44i−4i4i−4i4-44i−4i00000000111-1-1-1i−ii−ii−i0000111-1-1-1i−ii−ii−i000−i3i3−i3i3−i3i303−33−33−30000000000000000
χ464-44i−4i44-4-44i−4i4i−4i4-44i−4i00000000111-1-1-1i−ii−ii−i0000111-1-1-1i−ii−ii−i000i3−i3i3−i3i3−i30−33−33−330000000000000000
χ474-44i−4i44-4-44i−4i4i−4i4-44i−4i00000000-2-2-2222−2i2i−2i2i−2i2i0000-2-2-2222−2i2i−2i2i−2i2i00000000000000000000000000000000
χ484-44i−4i4-2-424i−4i−2i2i-22−2i2i00000000-2-2-2222−2i2i−2i2i−2i2i0000111-1-1-1i−ii−ii−i00000000000000000000006−6i6−i6000000
χ494-44i−4i4-2-424i−4i−2i2i-22−2i2i00000000-2-2-2222−2i2i−2i2i−2i2i0000111-1-1-1i−ii−ii−i0000000000000000000000−66−i6i6000000
χ504-44i−4i-242-4−2i2i4i−4i-22−2i2i0000−2i32i323−2311-2-1-12i−ii−i−2i2i000011-2-1-12i−ii−i−2i2i000−i3i3i3−i30003−3−33000000000000000000
χ514-44i−4i-242-4−2i2i4i−4i-22−2i2i0000−2i32i323−231-21-12-1i−i−2i2ii−i00001-21-12-1i−i−2i2ii−i000i3−i300−i3i30−33003−30000000000000000
χ524-44i−4i-242-4−2i2i4i−4i-22−2i2i0000−2i32i323−23-2112-1-1−2i2ii−ii−i0000-2112-1-1−2i2ii−ii−i00000−i3i3i3−i30003−3−330000000000000000
χ534-44i−4i-242-4−2i2i4i−4i-22−2i2i00002i3−2i3−232311-2-1-12i−ii−i−2i2i000011-2-1-12i−ii−i−2i2i000i3−i3−i3i3000−333−3000000000000000000
χ544-44i−4i-242-4−2i2i4i−4i-22−2i2i00002i3−2i3−23231-21-12-1i−i−2i2ii−i00001-21-12-1i−i−2i2ii−i000−i3i300i3−i303−300−330000000000000000
χ554-44i−4i-242-4−2i2i4i−4i-22−2i2i00002i3−2i3−2323-2112-1-1−2i2ii−ii−i0000-2112-1-1−2i2ii−ii−i00000i3−i3−i3i3000−333−30000000000000000
χ564-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i00000000111-1-1-1−ii−ii−ii0000111-1-1-1−ii−ii−ii000−i3i3−i3i3−i3i30−33−33−330000000000000000
χ574-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i00000000111-1-1-1−ii−ii−ii0000111-1-1-1−ii−ii−ii000i3−i3i3−i3i3−i303−33−33−30000000000000000
χ584-4−4i4i44-4-4−4i4i−4i4i4-4−4i4i00000000-2-2-22222i−2i2i−2i2i−2i0000-2-2-22222i−2i2i−2i2i−2i00000000000000000000000000000000
χ594-4−4i4i4-2-42−4i4i2i−2i-222i−2i00000000-2-2-22222i−2i2i−2i2i−2i0000111-1-1-1−ii−ii−ii00000000000000000000006−6−i6i6000000
χ604-4−4i4i4-2-42−4i4i2i−2i-222i−2i00000000-2-2-22222i−2i2i−2i2i−2i0000111-1-1-1−ii−ii−ii0000000000000000000000−66i6−i6000000
χ614-4−4i4i-242-42i−2i−4i4i-222i−2i0000−2i32i3−232311-2-1-12−ii−ii2i−2i000011-2-1-12−ii−ii2i−2i000−i3i3i3−i3000−333−3000000000000000000
χ624-4−4i4i-242-42i−2i−4i4i-222i−2i0000−2i32i3−23231-21-12-1−ii2i−2i−ii00001-21-12-1−ii2i−2i−ii000i3−i300−i3i303−300−330000000000000000
χ634-4−4i4i-242-42i−2i−4i4i-222i−2i0000−2i32i3−2323-2112-1-12i−2i−ii−ii0000-2112-1-12i−2i−ii−ii00000−i3i3i3−i3000−333−30000000000000000
χ644-4−4i4i-242-42i−2i−4i4i-222i−2i00002i3−2i323−2311-2-1-12−ii−ii2i−2i000011-2-1-12−ii−ii2i−2i000i3−i3−i3i30003−3−33000000000000000000
χ654-4−4i4i-242-42i−2i−4i4i-222i−2i00002i3−2i323−231-21-12-1−ii2i−2i−ii00001-21-12-1−ii2i−2i−ii000−i3i300i3−i30−33003−30000000000000000
χ664-4−4i4i-242-42i−2i−4i4i-222i−2i00002i3−2i323−23-2112-1-12i−2i−ii−ii0000-2112-1-12i−2i−ii−ii00000i3−i3−i3i30003−3−330000000000000000
χ6766666-36-366-3-3-3-3-3-3-200-20000000000000000-21-210000000000000010000001000000220-2-201111-1-10000
χ6866666-36-366-3-3-3-3-3-3-200-20000000000000000-21-210000000000000010000001000000-2-20220-1-1-1-1110000
χ696666-36-36-3-366-3-3-3-3-266-2-3-3-3-30000000000001-21-2000000000000-2-2100000010000000010010000000000
χ706666-36-36-3-366-3-3-3-3-2-6-6-233330000000000001-21-2000000000000221000000100000000-100-10000000000
χ7166-6-66-36-3-6-633-3-333200-200000000000000002-1-2100000000000000-100000010000002-20-22011-1-1-110000
χ7266-6-66-36-3-6-633-3-333200-200000000000000002-1-2100000000000000-10000001000000-2202-20-1-1111-10000
χ7366-6-6-36-3633-6-6-3-33326-6-2-3-333000000000000-121-20000000000002-2-1000000100000000-10010000000000
χ7466-6-6-36-3633-6-6-3-3332-66-233-3-3000000000000-121-2000000000000-22-1000000100000000100-10000000000
χ758-88i−8i8-4-848i−8i−4i4i-44−4i4i00000000222-2-2-22i−2i2i−2i2i−2i0000-1-1-1111−ii−ii−ii00000000000000000000000000000000
χ768-88i−8i-4-444−4i4i−4i4i2-22i−2i0000000022-4-2-242i−2i2i−2i−4i4i0000-1-1211-2−ii−ii2i−2i00000000000000000000000000000000
χ778-88i−8i-4-444−4i4i−4i4i2-22i−2i000000002-42-24-22i−2i−4i4i2i−2i0000-12-11-21−ii2i−2i−ii00000000000000000000000000000000
χ788-88i−8i-4-444−4i4i−4i4i2-22i−2i00000000-4224-2-2−4i4i2i−2i2i−2i00002-1-1-2112i−2i−ii−ii00000000000000000000000000000000
χ798-8−8i8i8-4-84−8i8i4i−4i-444i−4i00000000222-2-2-2−2i2i−2i2i−2i2i0000-1-1-1111i−ii−ii−i00000000000000000000000000000000
χ808-8−8i8i-4-4444i−4i4i−4i2-2−2i2i0000000022-4-2-24−2i2i−2i2i4i−4i0000-1-1211-2i−ii−i−2i2i00000000000000000000000000000000
χ818-8−8i8i-4-4444i−4i4i−4i2-2−2i2i000000002-42-24-2−2i2i4i−4i−2i2i0000-12-11-21i−i−2i2ii−i00000000000000000000000000000000
χ828-8−8i8i-4-4444i−4i4i−4i2-2−2i2i00000000-4224-2-24i−4i−2i2i−2i2i00002-1-1-211−2i2ii−ii−i00000000000000000000000000000000
χ8312121212-6-6-6-6-6-6-6-63333-400-40000000000000000222200000000000000-1000000-10000000000000000000000
χ841212-12-12-6-6-6-6666633-3-3400-40000000000000000-2-222000000000000001000000-10000000000000000000000

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