Finite Group Databasebeta

← Group #102196

Character table — Group #102196

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000000022-2-222-2-2000000000000
χ20222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2000000000000000000000000-2-222-2-222000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-2-2-22222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222222222-2-222-2-2000000000000000022-2-2-2-22200000000000000000000
χ2622222222-2-2-2-2-2-2-2-222222222-2-222-2-20000000000000000-2-22222-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-2-222-2-2000022-2-200002i2i−2i−2i00002i−2i00002i2i−2i−2i22-2-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3022-2-222-2-2000022-2-200002i2i−2i−2i00002i−2i00002i2i−2i−2i22-2-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3122-2-222-2-2000022-2-200002i2i−2i−2i00002i−2i0000−2i−2i2i2i-2-22200001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ3222-2-222-2-2000022-2-200002i2i−2i−2i00002i−2i0000−2i−2i2i2i-2-2220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ3322-2-222-2-2000022-2-20000−2i−2i2i2i0000−2i2i00002i2i−2i−2i-2-22200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3422-2-222-2-2000022-2-20000−2i−2i2i2i0000−2i2i00002i2i−2i−2i-2-2220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3522-2-222-2-2000022-2-20000−2i−2i2i2i0000−2i2i0000−2i−2i2i2i22-2-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ3622-2-222-2-2000022-2-20000−2i−2i2i2i0000−2i2i0000−2i−2i2i2i22-2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ3722-2-222-2-20000-2-22200002i2i−2i−2i0000−2i2i2i2i−2i−2i0000000022-2-21+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ3822-2-222-2-20000-2-22200002i2i−2i−2i0000−2i2i2i2i−2i−2i0000000022-2-2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ3922-2-222-2-20000-2-22200002i2i−2i−2i0000−2i2i−2i−2i2i2i00000000-2-2221+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ4022-2-222-2-20000-2-22200002i2i−2i−2i0000−2i2i−2i−2i2i2i00000000-2-222−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ4122-2-222-2-20000-2-2220000−2i−2i2i2i00002i−2i2i2i−2i−2i00000000-2-2221−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ4222-2-222-2-20000-2-2220000−2i−2i2i2i00002i−2i2i2i−2i−2i00000000-2-222−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ4322-2-222-2-20000-2-2220000−2i−2i2i2i00002i−2i−2i−2i2i2i0000000022-2-21−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ4422-2-222-2-20000-2-2220000−2i−2i2i2i00002i−2i−2i−2i2i2i0000000022-2-2−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ452-22-22-22-22i2i−2i−2i2-22-22i2i−2i−2i000000000000002-22-200002i−2i2i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ462-22-22-22-22i2i−2i−2i2-22-22i2i−2i−2i000000000000002-22-200002i−2i2i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ472-22-22-22-22i2i−2i−2i2-22-22i2i−2i−2i00000000000000-22-220000−2i2i−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ482-22-22-22-22i2i−2i−2i2-22-22i2i−2i−2i00000000000000-22-220000−2i2i−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ492-22-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i000000000000002-22-20000−2i2i−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ502-22-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i000000000000002-22-20000−2i2i−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ512-22-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i00000000000000-22-2200002i−2i2i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ522-22-22-22-2−2i−2i2i2i2-22-2−2i−2i2i2i00000000000000-22-2200002i−2i2i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ534444-4-4-4-44-44-4000000004-44-44-4000000000000000000000000000000000000000000000000
χ544444-4-4-4-44-44-400000000-44-44-44000000000000000000000000000000000000000000000000
χ554444-4-4-4-4-44-44000000004-44-4-44000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-44-4400000000-44-444-4000000000000000000000000000000000000000000000000
χ5744-4-4-4-444000000004i−4i4i−4i4i−4i−4i4i004-40000000000000000000000000000000000000000000000
χ5844-4-4-4-444000000004i−4i4i−4i−4i4i4i−4i00-440000000000000000000000000000000000000000000000
χ5944-4-4-4-44400000000−4i4i−4i4i4i−4i−4i4i00-440000000000000000000000000000000000000000000000
χ6044-4-4-4-44400000000−4i4i−4i4i−4i4i4i−4i004-40000000000000000000000000000000000000000000000
χ614-44-44-44-44i4i−4i−4i-44-44−4i−4i4i4i000000000000000000000000000000000000000000000000000000
χ624-44-44-44-4−4i−4i4i4i-44-444i4i−4i−4i000000000000000000000000000000000000000000000000000000
χ634-44-4-44-444i−4i−4i4i00000000000000000022−2222−2200002i2−2i22i2−2i200000000000000000000000000000000
χ644-44-4-44-444i−4i−4i4i000000000000000000−2222−22220000−2i22i2−2i22i200000000000000000000000000000000
χ654-44-4-44-44−4i4i4i−4i00000000000000000022−2222−220000−2i22i2−2i22i200000000000000000000000000000000
χ664-44-4-44-44−4i4i4i−4i000000000000000000−2222−222200002i2−2i22i2−2i200000000000000000000000000000000
χ674-4-444-4-4400004-4-440000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ684-4-444-4-4400004-4-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ694-4-444-4-440000-444-4000000000000000000000000004i−4i−4i4i0000000000000000000000000000
χ704-4-444-4-440000-444-400000000000000000000000000−4i4i4i−4i0000000000000000000000000000
χ714-4-44-444-4000000004-4-4400000000002i2−2i2−2i22i20000−2i22i22i2−2i200000000000000000000000000000000
χ724-4-44-444-4000000004-4-440000000000−2i22i22i2−2i200002i2−2i2−2i22i200000000000000000000000000000000
χ734-4-44-444-400000000-444-400000000002i2−2i2−2i22i200002i2−2i2−2i22i200000000000000000000000000000000
χ744-4-44-444-400000000-444-40000000000−2i22i22i2−2i20000−2i22i22i2−2i200000000000000000000000000000000

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