Finite Group Databasebeta

← Group #13180041

Character table — Group #13180041

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size12336691212121218181824242424242454547272727296961233669121212121818182424242424245454727272729696
order132266233662463666662466121233262266266662466666662466121266
χ111111111111111111111111111111111111111111111111111111111
χ211111111111-1-11111111-1-1-1-1-1-11111111111111-1-11111111-1-1-1-1-1-111
χ31111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ41111111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32111-1-11−i321+i321−i321+i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32111-1-11−i321+i321−i321+i32−1+i32−1−i32
χ51111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ61111111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32111-1-11+i321−i321+i321−i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32111-1-11+i321−i321+i321−i32−1−i32−1+i32
χ722222222222002-122-1-1-1000000-1-122222222222002-122-1-1-1000000-1-1
χ82222222−1+i3−1−i3−1+i3−1−i3002-1−1+i3−1−i3-1-1-10000001−i321+i322222222−1+i3−1−i3−1+i3−1−i3002-1−1+i3−1−i3-1-1-10000001−i321+i32
χ92222222−1−i3−1+i3−1−i3−1+i3002-1−1−i3−1+i3-1-1-10000001+i321−i322222222−1−i3−1+i3−1−i3−1+i3002-1−1−i3−1+i3-1-1-10000001+i321−i32
χ10333-13-1-133-1-11-1-10-1-10001-111-1-100333-13-1-133-1-11-1-10-1-10001-111-1-100
χ11333-13-1-133-1-1-11-10-1-1000-11-1-11100333-13-1-133-1-1-11-10-1-1000-11-1-11100
χ12333-13-1-1−3+3i32−3−3i321−i321+i321-1-101−i321+i320001-1−1+i32−1−i321−i321+i3200333-13-1-1−3+3i32−3−3i321−i321+i321-1-101−i321+i320001-1−1+i32−1−i321−i321+i3200
χ13333-13-1-1−3+3i32−3−3i321−i321+i32-11-101−i321+i32000-111−i321+i32−1+i32−1−i3200333-13-1-1−3+3i32−3−3i321−i321+i32-11-101−i321+i32000-111−i321+i32−1+i32−1−i3200
χ14333-13-1-1−3−3i32−3+3i321+i321−i321-1-101+i321−i320001-1−1−i32−1+i321+i321−i3200333-13-1-1−3−3i32−3+3i321+i321−i321-1-101+i321−i320001-1−1−i32−1+i321+i321−i3200
χ15333-13-1-1−3−3i32−3+3i321+i321−i32-11-101+i321−i32000-111+i321−i32−1−i32−1+i3200333-13-1-1−3−3i32−3+3i321+i321−i32-11-101+i321−i32000-111+i321−i32−1−i32−1+i3200
χ1633-13-13-1000033-1300-1-1-1-1-100000033-13-13-1000033-1300-1-1-1-1-1000000
χ1733-13-13-10000-3-3-1300-1-1-11100000033-13-13-10000-3-3-1300-1-1-111000000
χ1866-26-26-2000000-2-3001110000000066-26-26-2000000-2-30011100000000
χ196-366-3-36000000-3000000000000006-366-3-36000000-300000000000000
χ206-36-2-31-200440010-2-2000000000006-36-2-31-200440010-2-200000000000
χ216-36-2-31-200−2+2i3−2−2i300101−i31+i3000000000006-36-2-31-200−2+2i3−2−2i300101−i31+i300000000000
χ226-36-2-31-200−2−2i3−2+2i300101+i31−i3000000000006-36-2-31-200−2−2i3−2+2i300101+i31−i300000000000
χ236-3-261-3-200000010004-2-2000000006-3-261-3-200000010004-2-200000000
χ246-3-261-3-20000001000-24-2000000006-3-261-3-20000001000-24-200000000
χ256-3-261-3-20000001000-2-24000000006-3-261-3-20000001000-2-2400000000
χ2699-3-3-3-3100003-31000000-1100000099-3-3-3-3100003-31000000-11000000
χ2799-3-3-3-310000-3310000001-100000099-3-3-3-310000-3310000001-1000000
χ2818-9-6-6332000000-10000000000000018-9-6-6332000000-100000000000000
χ291111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3011111111111-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1
χ311111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-11−i321+i32-1-1-1-1-11−i321+i321−i321+i321−i321+i32
χ321111111−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32111-1-11−i321+i321−i321+i32−1+i32−1−i32-1-1-1-1-1-1-11−i321+i321−i321+i3211-1-11−i321+i32-1-1-111−1+i32−1−i32−1+i32−1−i321−i321+i32
χ331111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-11+i321−i32-1-1-1-1-11+i321−i321+i321−i321+i321−i32
χ341111111−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32111-1-11+i321−i321+i321−i32−1−i32−1+i32-1-1-1-1-1-1-11+i321−i321+i321−i3211-1-11+i321−i32-1-1-111−1−i32−1+i32−1−i32−1+i321+i321−i32
χ3522222222222002-122-1-1-1000000-1-1-2-2-2-2-2-2-2-2-2-2-200-21-2-211100000011
χ362222222−1+i3−1−i3−1+i3−1−i3002-1−1+i3−1−i3-1-1-10000001−i321+i32-2-2-2-2-2-2-21−i31+i31−i31+i300-211−i31+i3111000000−1+i32−1−i32
χ372222222−1−i3−1+i3−1−i3−1+i3002-1−1−i3−1+i3-1-1-10000001+i321−i32-2-2-2-2-2-2-21+i31−i31+i31−i300-211+i31−i3111000000−1−i32−1+i32
χ38333-13-1-133-1-11-1-10-1-10001-111-1-100-3-3-31-311-3-311-111011000-11-1-11100
χ39333-13-1-133-1-1-11-10-1-1000-11-1-11100-3-3-31-311-3-3111-110110001-111-1-100
χ40333-13-1-1−3+3i32−3−3i321−i321+i321-1-101−i321+i320001-1−1+i32−1−i321−i321+i3200-3-3-31-3113−3i323+3i32−1+i32−1−i32-1110−1+i32−1−i32000-111−i321+i32−1+i32−1−i3200
χ41333-13-1-1−3+3i32−3−3i321−i321+i32-11-101−i321+i32000-111−i321+i32−1+i32−1−i3200-3-3-31-3113−3i323+3i32−1+i32−1−i321-110−1+i32−1−i320001-1−1+i32−1−i321−i321+i3200
χ42333-13-1-1−3−3i32−3+3i321+i321−i321-1-101+i321−i320001-1−1−i32−1+i321+i321−i3200-3-3-31-3113+3i323−3i32−1−i32−1+i32-1110−1−i32−1+i32000-111+i321−i32−1−i32−1+i3200
χ43333-13-1-1−3−3i32−3+3i321+i321−i32-11-101+i321−i32000-111+i321−i32−1−i32−1+i3200-3-3-31-3113+3i323−3i32−1−i32−1+i321-110−1−i32−1+i320001-1−1−i32−1+i321+i321−i3200
χ4433-13-13-1000033-1300-1-1-1-1-1000000-3-31-31-310000-3-31-30011111000000
χ4533-13-13-10000-3-3-1300-1-1-111000000-3-31-31-310000331-300111-1-1000000
χ4666-26-26-2000000-2-30011100000000-6-62-62-620000002300-1-1-100000000
χ476-366-3-36000000-300000000000000-63-6-633-6000000300000000000000
χ486-36-2-31-200440010-2-200000000000-63-623-1200-4-400-102200000000000
χ496-36-2-31-200−2+2i3−2−2i300101−i31+i300000000000-63-623-12002−2i32+2i300-10−1+i3−1−i300000000000
χ506-36-2-31-200−2−2i3−2+2i300101+i31−i300000000000-63-623-12002+2i32−2i300-10−1−i3−1+i300000000000
χ516-3-261-3-200000010004-2-200000000-632-6-132000000-1000-42200000000
χ526-3-261-3-20000001000-24-200000000-632-6-132000000-10002-4200000000
χ536-3-261-3-20000001000-2-2400000000-632-6-132000000-100022-400000000
χ5499-3-3-3-3100003-31000000-11000000-9-93333-10000-33-10000001-1000000
χ5599-3-3-3-310000-3310000001-1000000-9-93333-100003-3-1000000-11000000
χ5618-9-6-6332000000-100000000000000-18966-3-3-2000000100000000000000

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