Finite Group Databasebeta

← Group #150901

Character table — Group #150901

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444444444888888888888888888888161616161616323232323232
order124424888824444488882244816161616161616161616161616161616888888444444
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111-1-1-1-1-1-1-1-11-11-11iiiiiiii−i−i−i−i−i−i−i−i11111-1-1-1ii−i−i
χ6111111111111-1-1-1-1-1-1-1-11-11-11iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11-111−i−iii
χ7111111111111-1-1-1-1-1-1-1-11-11-11−i−i−i−i−i−i−i−iiiiiiiii11111-1-1-1−i−iii
χ8111111111111-1-1-1-1-1-1-1-11-11-11−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11-111ii−i−i
χ9111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1111-1i−ii−i
χ10111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-11−ii−ii
χ11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1111-1−ii−ii
χ12111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-11i−ii−i
χ13111111-1-1-1-111-1-1-1-11111-11-11-11111-1-1-1-1-1-1-1-1111111-1-11-1-111-1-11
χ14111111-1-1-1-111-1-1-1-11111-11-11-11111-1-1-1-1-1-1-1-11111-1-1111-11-1-111-1
χ15111111-1-1-1-111-1-1-1-11111-11-11-1-1-1-1-111111111-1-1-1-111-1-11-1-11-111-1
χ16111111-1-1-1-111-1-1-1-11111-11-11-1-1-1-1-111111111-1-1-1-1-1-1111-11-11-1-11
χ1722222222222222222222-2-2-2-2200000000000000000000-2-2000000
χ18222222222222-2-2-2-2-2-2-2-2-22-22200000000000000000000-22000000
χ19222222-2-2-2-2222222-2-2-2-22222-200000000000000000000-2-2000000
χ20222222-2-2-2-222-2-2-2-222222-22-2-200000000000000000000-22000000
χ2122-2-22-20000-2222-2-2000022-2-20i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2222-2-22-20000-2222-2-2000022-2-20−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2322-2-22-20000-2222-2-20000-2-222022−2−2−2−22222−2−2−2−222000000000000
χ2422-2-22-20000-2222-2-20000-2-2220−2−22222−2−2−2−22222−2−2000000000000
χ2522-2-22-20000-22-2-22200002-2-22022−2−222−2−2−2−222−2−222000000000000
χ2622-2-22-20000-22-2-22200002-2-220−2−222−2−22222−2−222−2−2000000000000
χ2722-2-22-20000-22-2-2220000-222-20i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822-2-22-20000-22-2-2220000-222-20−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ294444444444-4-4000000000000-40000000000000000000000000000
χ30444444-4-4-4-4-4-400000000000040000000000000000000000000000
χ3144-4-44-400004-400004i4i−4i−4i000000000000000000000000000000000
χ3244-4-44-400004-40000−4i−4i4i4i000000000000000000000000000000000
χ3344-4-4-4444-4-400000000000000000000000000000002i−2i2i−2i00000000
χ3444-4-4-4444-4-40000000000000000000000000000000−2i2i−2i2i00000000
χ3544-4-4-44-4-44400000000000000000000000000000002i−2i−2i2i00000000
χ3644-4-4-44-4-4440000000000000000000000000000000−2i2i2i−2i00000000
χ374-44i−4i002i2−2i222−22002-22i−2i2ζ2−2ζ22ζ6−2ζ600000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7000000000000
χ384-44i−4i002i2−2i222−22002-22i−2i2ζ2−2ζ22ζ6−2ζ600000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7000000000000
χ394-44i−4i002i2−2i222−2200-22−2i2i−2ζ22ζ2−2ζ62ζ600000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7000000000000
χ404-44i−4i002i2−2i222−2200-22−2i2i−2ζ22ζ2−2ζ62ζ600000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7000000000000
χ414-44i−4i00−2i22i2−2222002-22i−2i−2ζ22ζ2−2ζ62ζ600000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7000000000000
χ424-44i−4i00−2i22i2−2222002-22i−2i−2ζ22ζ2−2ζ62ζ600000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7000000000000
χ434-44i−4i00−2i22i2−222200-22−2i2i2ζ2−2ζ22ζ6−2ζ600000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7000000000000
χ444-44i−4i00−2i22i2−222200-22−2i2i2ζ2−2ζ22ζ6−2ζ600000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7000000000000
χ454-4−4i4i002i2−2i2−2222002-2−2i2i2ζ6−2ζ62ζ2−2ζ200000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5000000000000
χ464-4−4i4i002i2−2i2−2222002-2−2i2i2ζ6−2ζ62ζ2−2ζ200000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5000000000000
χ474-4−4i4i002i2−2i2−222200-222i−2i−2ζ62ζ6−2ζ22ζ200000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5000000000000
χ484-4−4i4i002i2−2i2−222200-222i−2i−2ζ62ζ6−2ζ22ζ200000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5000000000000
χ494-4−4i4i00−2i22i222−22002-2−2i2i−2ζ62ζ6−2ζ22ζ200000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5000000000000
χ504-4−4i4i00−2i22i222−22002-2−2i2i−2ζ62ζ6−2ζ22ζ200000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5000000000000
χ514-4−4i4i00−2i22i222−2200-222i−2i2ζ6−2ζ62ζ2−2ζ200000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5000000000000
χ524-4−4i4i00−2i22i222−2200-222i−2i2ζ6−2ζ62ζ2−2ζ200000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5000000000000
χ538888-8-800000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.