Finite Group Databasebeta

← Group #152212

Character table — Group #152212

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222244444444444222244444444444448888888888884444
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-111111-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1
χ4111111111111111111-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-111-1-1-111-11111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ611111111111-1-111-1-1-111-11111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ711111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ811111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ9111111-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-111-1-111-1-111-1-11-11-1
χ10111111-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-111-1-1-1-111-1-111-11-11
χ11111111-1-1-1-1-11111111-1-1111-1-1-1-11111-1-1-1-1-11111-1-111-1-1-11-11
χ12111111-1-1-1-1-11111111-1-1111-1-1-1-11111-1-1-1-1-111-1-111-1-1111-11-1
χ13111111-1-1-1-1-1-1-111-1-1-111-111-1-111-1-1-1-1111-1-111ii−i−i−i−iiii−i−ii
χ14111111-1-1-1-1-1-1-111-1-1-111-111-1-111-1-1-1-1111-1-111−i−iiiii−i−i−iii−i
χ15111111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111-1-1ii−i−i−i−iii−iii−i
χ16111111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222222-200-2-2-2-2-200000022-20000000000000000
χ1822222222222-2-222-2-22002-2-2-2-2000000-2-220000000000000000
χ19222222-2-2-2-2-2222222-200-2-2-222000000-2-220000000000000000
χ20222222-2-2-2-2-2-2-222-2-22002-2-22200000022-20000000000000000
χ2122-2-22-200000222-2-2-222-2-22-2002-200000002-200000000000000
χ2222-2-22-200000222-2-2-22-22-22-200-220000000-2200000000000000
χ2322-2-22-200000222-2-2-2-2002-2200002i2i−2i−2i000002i−2i000000000000
χ2422-2-22-200000222-2-2-2-2002-220000−2i−2i2i2i00000−2i2i000000000000
χ2522-2-22-200000-2-22-222200-2-2200002i2i−2i−2i00000−2i2i000000000000
χ2622-2-22-200000-2-22-222200-2-220000−2i−2i2i2i000002i−2i000000000000
χ2722-2-22-200000-2-22-222-22-222-2002-20000000-2200000000000000
χ2822-2-22-200000-2-22-222-2-2222-200-2200000002-200000000000000
χ29444444444-4-400-4-400000000000000000000000000000000000
χ30444444-4-4-44400-4-400000000000000000000000000000000000
χ314444-4-444-40000000002200000-2-22-22-20000000000000000000
χ324444-4-444-4000000000-2-20000022-22-220000000000000000000
χ334444-4-4-4-440000000002200000-2-2-22-220000000000000000000
χ344444-4-4-4-44000000000-2-200000222-22-20000000000000000000
χ3544-4-44-40000000-44000000004i−4i0000000000000000000000000
χ3644-4-44-40000000-4400000000−4i4i0000000000000000000000000
χ3744-4-4-440004i−4i00000002-200000-222i−2i−2i2i0000000000000000000
χ3844-4-4-440004i−4i0000000-22000002-2−2i2i2i−2i0000000000000000000
χ3944-4-4-44000−4i4i00000002-200000-22−2i2i2i−2i0000000000000000000
χ4044-4-4-44000−4i4i0000000-22000002-22i−2i−2i2i0000000000000000000
χ414-44-4004i−4i0002i−2i002i−2i000000000000002-2000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ424-44-4004i−4i0002i−2i002i−2i000000000000002-200000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ434-44-4004i−4i000−2i2i00−2i2i00000000000000-22000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ444-44-4004i−4i000−2i2i00−2i2i00000000000000-2200000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ454-44-400−4i4i0002i−2i002i−2i00000000000000-22000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ464-44-400−4i4i0002i−2i002i−2i00000000000000-2200000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ474-44-400−4i4i000−2i2i00−2i2i000000000000002-2000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ484-44-400−4i4i000−2i2i00−2i2i000000000000002-200000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ498-8-8800000004i−4i00−4i4i000000000000000000000000000000000
χ508-8-880000000−4i4i004i−4i000000000000000000000000000000000

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