Finite Group Databasebeta

← Group #94191

Character table — Group #94191

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244224444444444444448888888824444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1iiii−i−i−i−iii−i−i
χ61111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1−i−i−i−iiiii−i−iii
χ71111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ81111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-1-1-111-1111111-1-1-1-1-1-1iiii−i−i−i−i1ii−i−i11-1-111-1-1i−ii−i
χ10111111-1-1-1-111-1111111-1-1-1-1-1-1iiii−i−i−i−i1ii−i−i-1-111-1-111−ii−ii
χ11111111-1-1-1-111-1111111-1-1-1-1-1-1−i−i−i−iiiii1−i−iii11-1-111-1-1−ii−ii
χ12111111-1-1-1-111-1111111-1-1-1-1-1-1−i−i−i−iiiii1−i−iii-1-111-1-111i−ii−i
χ13111111-1-1-1-111-1-1-1-1-111-1-11111iiii−i−i−i−i-1−i−iiiii−i−i−i−iii-111-1
χ14111111-1-1-1-111-1-1-1-1-111-1-11111iiii−i−i−i−i-1−i−iii−i−iiiii−i−i1-1-11
χ15111111-1-1-1-111-1-1-1-1-111-1-11111−i−i−i−iiiii-1ii−i−iii−i−i−i−iii1-1-11
χ16111111-1-1-1-111-1-1-1-1-111-1-11111−i−i−i−iiiii-1ii−i−i−i−iiiii−i−i-111-1
χ1722222222222222222-2-2-2-222-2-200000000-20000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2220000000020000000000000000
χ19222222-2-2-2-222-22222-2-222-2-22200000000-20000000000000000
χ20222222-2-2-2-222-2-2-2-2-2-2-22222-2-20000000020000000000000000
χ212-2-222-200002-202i−2i2i−2i002i−2i002-21+i1+i−1−i−1−i1−i1−i−1+i−1+i01−i−1+i1+i−1−i000000000000
χ222-2-222-200002-202i−2i2i−2i002i−2i002-2−1−i−1−i1+i1+i−1+i−1+i1−i1−i0−1+i1−i−1−i1+i000000000000
χ232-2-222-200002-202i−2i2i−2i00−2i2i00-221−i1−i−1+i−1+i1+i1+i−1−i−1−i0−1−i1+i−1+i1−i000000000000
χ242-2-222-200002-202i−2i2i−2i00−2i2i00-22−1+i−1+i1−i1−i−1−i−1−i1+i1+i01+i−1−i1−i−1+i000000000000
χ252-2-222-200002-20−2i2i−2i2i002i−2i00-221+i1+i−1−i−1−i1−i1−i−1+i−1+i0−1+i1−i−1−i1+i000000000000
χ262-2-222-200002-20−2i2i−2i2i002i−2i00-22−1−i−1−i1+i1+i−1+i−1+i1−i1−i01−i−1+i1+i−1−i000000000000
χ272-2-222-200002-20−2i2i−2i2i00−2i2i002-21−i1−i−1+i−1+i1+i1+i−1−i−1−i01+i−1−i1−i−1+i000000000000
χ282-2-222-200002-20−2i2i−2i2i00−2i2i002-2−1+i−1+i1−i1−i−1−i−1−i1+i1+i0−1−i1+i−1+i1−i000000000000
χ2944444444-4-4-4-440000000000000000000000000000000000000
χ30444444-4-444-4-4-40000000000000000000000000000000000000
χ314444-4-4440000-40000000000002-22-22-22-200000000000000000
χ324444-4-4440000-4000000000000-22-22-22-2200000000000000000
χ334444-4-4-4-4000040000000000002i−2i2i−2i−2i2i−2i2i00000000000000000
χ344444-4-4-4-400004000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000
χ3544-4-4004i−4i000002i−2i−2i2i00002-20000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ3644-4-4004i−4i000002i−2i−2i2i00002-2000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ3744-4-4004i−4i00000−2i2i2i−2i0000-220000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ3844-4-4004i−4i00000−2i2i2i−2i0000-22000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ3944-4-400−4i4i000002i−2i−2i2i0000-220000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ4044-4-400−4i4i000002i−2i−2i2i0000-22000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ4144-4-400−4i4i00000−2i2i2i−2i00002-20000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ4244-4-400−4i4i00000−2i2i2i−2i00002-2000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ434-4-444-40000-44000004i−4i0000000000000000000000000000000
χ444-4-444-40000-4400000−4i4i0000000000000000000000000000000
χ454-4-44-44004-40000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000
χ464-4-44-44004-4000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000
χ474-4-44-4400-440000000000000002-2-222-2-2200000000000000000
χ484-4-44-4400-44000000000000000-222-2-222-200000000000000000
χ498-88-800000000044-4-4000000000000000000000000000000000
χ508-88-8000000000-4-444000000000000000000000000000000000

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