Finite Group Databasebeta

← Group #116551

Character table — Group #116551

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444888888888888888888888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−iii−i−i11-1-1
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−i−iii−i−iii-1-111
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii−i−iii11-1-1
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11ii−i−iii−i−i-1-111
χ1311111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-11-1ii−i−i−i−iii-1-111
χ1411111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-11-11−i−iiiii−i−i11-1-1
χ1511111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-11-1−i−iiiii−i−i-1-111
χ1611111111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i−i−iii11-1-1
χ172222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222000000000000000000000000000000000000000000002i−2i2i−2i
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000000−2i2i−2i2i
χ19222222222222-2-2-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-222222-2-2-2-2222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-22222-2-2-222-2-2000000000000000000000000000000002-2-22000000000000
χ22222222222222-2-2-2-2-2-2-2-2-22222-2-2-222-2-200000000000000000000000000000000-222-2000000000000
χ2322222222-2-2-2-22222-222222222-2-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i−2i2i
χ2422222222-2-2-2-22222-222222222-2-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i2i−2i
χ2522222222-2-2-2-2-2-2-2-22-2-2-2-22222222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22-2-2-2-22222222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-222220000000000000000000000000000000022-2-2000000000000
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2222200000000000000000000000000000000-2-222000000000000
χ29222-2-2-2-222-22-20000222-2-200002-2-2000000002i2i−2i−2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ30222-2-2-2-222-22-20000222-2-200002-2-2000000002i2i−2i−2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ31222-2-2-2-222-22-20000222-2-200002-2-200000000−2i−2i2i2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ32222-2-2-2-222-22-20000222-2-200002-2-200000000−2i−2i2i2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ33222-2-2-2-22-22-2200002-2-22200002-2-2000000002i2i−2i−2i0000−2i−2i2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ34222-2-2-2-22-22-2200002-2-22200002-2-2000000002i2i−2i−2i0000−2i−2i2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ35222-2-2-2-22-22-2200002-2-22200002-2-200000000−2i−2i2i2i00002i2i−2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ36222-2-2-2-22-22-2200002-2-22200002-2-200000000−2i−2i2i2i00002i2i−2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ372-2-222-2-222-2-22000022-22-20000-22-200002i2i−2i−2i00002i2i−2i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-222-2-222-2-22000022-22-20000-22-200002i2i−2i−2i00002i2i−2i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-222-2-222-2-22000022-22-20000-22-20000−2i−2i2i2i0000−2i−2i2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-222-2-222-2-22000022-22-20000-22-20000−2i−2i2i2i0000−2i−2i2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-222-2-22-222-200002-22-220000-22-200002i2i−2i−2i0000−2i−2i2i2i0000i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ422-2-222-2-22-222-200002-22-220000-22-200002i2i−2i−2i0000−2i−2i2i2i0000−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ432-2-222-2-22-222-200002-22-220000-22-20000−2i−2i2i2i00002i2i−2i−2i0000i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ442-2-222-2-22-222-200002-22-220000-22-20000−2i−2i2i2i00002i2i−2i−2i0000−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ452-2-2-2-222222-2-222-2-222-2-2222-2-2-2-222-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ462-2-2-2-222222-2-222-2-222-2-2222-2-2-2-222-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ472-2-2-2-222222-2-222-2-2-2-222-2-2-22222-2-222-20000000000000000000000000000000000002i−2i2i−2i00000000
χ482-2-2-2-222222-2-222-2-2-2-222-2-2-22222-2-222-2000000000000000000000000000000000000−2i2i−2i2i00000000
χ492-2-2-2-222222-2-2-2-22222-2-22-2-222-2-22-22-2200000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ502-2-2-2-222222-2-2-2-22222-2-22-2-222-2-22-22-220000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ512-2-2-2-222222-2-2-2-222-2-222-222-2-222-22-2-2200000000000000000000000000000000000000002i−2i2i−2i0000
χ522-2-2-2-222222-2-2-2-222-2-222-222-2-222-22-2-220000000000000000000000000000000000000000−2i2i−2i2i0000
χ532-2-2-2-2222-2-22222-2-22-222-2-2-222-2-222-2-220000000000000000000000002-2-22-222-20000000000000000
χ542-2-2-2-2222-2-22222-2-22-222-2-2-222-2-222-2-22000000000000000000000000-222-22-2-220000000000000000
χ552-2-2-2-2222-2-22222-2-2-22-2-2222-2-222-2-22-220000000000000000000000000000000000002-2-2200000000
χ562-2-2-2-2222-2-22222-2-2-22-2-2222-2-222-2-22-22000000000000000000000000000000000000-222-200000000
χ572-2-2-2-2222-2-222-2-2222-222-222-2-2-2-22-222-200000000000000002-2-22-222-2000000000000000000000000
χ582-2-2-2-2222-2-222-2-2222-222-222-2-2-2-22-222-20000000000000000-222-22-2-22000000000000000000000000
χ592-2-2-2-2222-2-222-2-222-22-2-22-2-22222-22-22-200000000000000000000000000000000000000002-2-220000
χ602-2-2-2-2222-2-222-2-222-22-2-22-2-22222-22-22-20000000000000000000000000000000000000000-222-20000
χ61444-4-4-4-444-44-40000-4-4-4440000-4440000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-44-440000-444-4-40000-4440000000000000000000000000000000000000000000000000000
χ6344-44-44-4-400000000000004i−4i4i−4i000000000002i2−2i22i2−2i222−2222−22000000000000000000000000000000000000
χ6444-44-44-4-400000000000004i−4i4i−4i00000000000−2i22i2−2i22i2−2222−2222000000000000000000000000000000000000
χ6544-44-44-4-40000000000000−4i4i−4i4i000000000002i2−2i22i2−2i2−2222−2222000000000000000000000000000000000000
χ6644-44-44-4-40000000000000−4i4i−4i4i00000000000−2i22i2−2i22i222−2222−22000000000000000000000000000000000000
χ6744-4-44-44-400004i−4i4i−4i00000000000000002i2−2i22i2−2i222−22−22220000000000000000000000000000000000000000
χ6844-4-44-44-400004i−4i4i−4i0000000000000000−2i22i2−2i22i2−222222−220000000000000000000000000000000000000000
χ6944-4-44-44-40000−4i4i−4i4i00000000000000002i2−2i22i2−2i2−222222−220000000000000000000000000000000000000000
χ7044-4-44-44-40000−4i4i−4i4i0000000000000000−2i22i2−2i22i222−22−22220000000000000000000000000000000000000000
χ714-444-4-44-400004i−4i−4i4i0000000000000000000000002i2−2i2−2i22i222−2222−2200000000000000000000000000000000
χ724-444-4-44-400004i−4i−4i4i000000000000000000000000−2i22i22i2−2i2−2222−222200000000000000000000000000000000
χ734-444-4-44-40000−4i4i4i−4i0000000000000000000000002i2−2i2−2i22i2−2222−222200000000000000000000000000000000
χ744-444-4-44-40000−4i4i4i−4i000000000000000000000000−2i22i22i2−2i222−2222−2200000000000000000000000000000000
χ754-44-444-4-400000000000004i−4i−4i4i000000022−22−222200000000−2i22i22i2−2i200000000000000000000000000000000
χ764-44-444-4-400000000000004i−4i−4i4i0000000−222222−22000000002i2−2i2−2i22i200000000000000000000000000000000
χ774-44-444-4-40000000000000−4i4i4i−4i000000022−22−2222000000002i2−2i2−2i22i200000000000000000000000000000000
χ784-44-444-4-40000000000000−4i4i4i−4i0000000−222222−2200000000−2i22i22i2−2i200000000000000000000000000000000
χ794-4-444-4-444-4-440000-4-44-4400004-440000000000000000000000000000000000000000000000000000
χ804-4-444-4-44-444-40000-44-44-400004-440000000000000000000000000000000000000000000000000000

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