Finite Group Databasebeta

← Group #142177

Character table — Group #142177

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244442222444444444444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i
χ9111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-222-2-2-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-222-2-2222222-2-222-2-200000000000000000000000000000000
χ21222-2-2-2-222-22-2000000002i−2i0022-2-22i−2i002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ22222-2-2-2-222-22-2000000002i−2i0022-2-22i−2i002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ23222-2-2-2-222-22-2000000002i−2i00-2-2222i−2i00−2i2i001+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i0000000000000000
χ24222-2-2-2-222-22-2000000002i−2i00-2-2222i−2i00−2i2i00−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i0000000000000000
χ25222-2-2-2-222-22-200000000−2i2i0022-2-2−2i2i00−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ26222-2-2-2-222-22-200000000−2i2i0022-2-2−2i2i00−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ27222-2-2-2-222-22-200000000−2i2i00-2-222−2i2i002i−2i001−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i0000000000000000
χ28222-2-2-2-222-22-200000000−2i2i00-2-222−2i2i002i−2i00−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i0000000000000000
χ2922-222-2-2-222-2-200002-22-222000000-2-22-2000000002-22-200002-22-20000000000000000
χ3022-222-2-2-222-2-200002-22-222000000-2-22-200000000-22-220000-22-220000000000000000
χ3122-222-2-2-222-2-200002-22-2-2-200000022-2200002i−2i2i−2i00002i−2i2i−2i00000000000000000000
χ3222-222-2-2-222-2-200002-22-2-2-200000022-220000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000
χ3322-222-2-2-222-2-20000-22-2222000000-2-2-2200002-22-20000-22-2200000000000000000000
χ3422-222-2-2-222-2-20000-22-2222000000-2-2-220000-22-2200002-22-200000000000000000000
χ3522-222-2-2-222-2-20000-22-22-2-2000000222-2000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ3622-222-2-2-222-2-20000-22-22-2-2000000222-200000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ3722-2-2-222-22-2-222i2i−2i−2i00002i−2i2i−2i0000−2i2i00002-21+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ3822-2-2-222-22-2-222i2i−2i−2i00002i−2i2i−2i0000−2i2i00002-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ3922-2-2-222-22-2-222i2i−2i−2i0000−2i2i2i−2i00002i−2i0000-221−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ4022-2-2-222-22-2-222i2i−2i−2i0000−2i2i2i−2i00002i−2i0000-22−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ4122-2-2-222-22-2-22−2i−2i2i2i00002i−2i−2i2i0000−2i2i0000-221+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ4222-2-2-222-22-2-22−2i−2i2i2i00002i−2i−2i2i0000−2i2i0000-22−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ4322-2-2-222-22-2-22−2i−2i2i2i0000−2i2i−2i2i00002i−2i00002-21−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ4422-2-2-222-22-2-22−2i−2i2i2i0000−2i2i−2i2i00002i−2i00002-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ4522-2-2-222-2-222-22i2i−2i−2i2-2-2200−2i2i2i−2i2i−2i000000000000000000000000000000002−2i2−i22−2i2−i2
χ4622-2-2-222-2-222-22i2i−2i−2i2-2-2200−2i2i2i−2i2i−2i00000000000000000000000000000000−22−i2i2−22−i2i2
χ4722-2-2-222-2-222-22i2i−2i−2i-222-200−2i2i−2i2i−2i2i00000000000000000000000000000000i2−i2−22−i2i22−2
χ4822-2-2-222-2-222-22i2i−2i−2i-222-200−2i2i−2i2i−2i2i00000000000000000000000000000000−i2i22−2i2−i2−22
χ4922-2-2-222-2-222-2−2i−2i2i2i2-2-22002i−2i−2i2i−2i2i000000000000000000000000000000002−2−i2i22−2−i2i2
χ5022-2-2-222-2-222-2−2i−2i2i2i2-2-22002i−2i−2i2i−2i2i00000000000000000000000000000000−22i2−i2−22i2−i2
χ5122-2-2-222-2-222-2−2i−2i2i2i-222-2002i−2i2i−2i2i−2i00000000000000000000000000000000i2−i22−2−i2i2−22
χ5222-2-2-222-2-222-2−2i−2i2i2i-222-2002i−2i2i−2i2i−2i00000000000000000000000000000000−i2i2−22i2−i22−2
χ5344444444-4-4-4-44444000000-4-400000000000000000000000000000000000000000000
χ5444444444-4-4-4-4-4-4-4-40000004400000000000000000000000000000000000000000000
χ55444-4-4-4-44-44-44000044-4-4000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-44-440000-4-444000000000000000000000000000000000000000000000000
χ5744-444-4-4-4-4-4440000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ5844-444-4-4-4-4-444000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ594-444-4-44-400004i−4i4i−4i0000000000000000000000000000000000002-22i−2i000000000000
χ604-444-4-44-400004i−4i4i−4i000000000000000000000000000000000000-22−2i2i000000000000
χ614-444-4-44-40000−4i4i−4i4i0000000000000000000000000000000000002-2−2i2i000000000000
χ624-444-4-44-40000−4i4i−4i4i000000000000000000000000000000000000-222i−2i000000000000
χ634-4-4-44-44400004-4-4400000000000000000000000000000000000000002-22-200000000
χ644-4-4-44-44400004-4-440000000000000000000000000000000000000000-22-2200000000
χ654-4-4-44-4440000-444-400000000000000000000000000000000000000002-2-2200000000
χ664-4-4-44-4440000-444-40000000000000000000000000000000000000000-222-200000000
χ678-88-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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