Finite Group Databasebeta

← Group #147621

Character table — Group #147621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222222222444444448888888822224444888888888888161616161616161616161616161616162244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ911111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−i−i−iii
χ1411111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i
χ1511111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-2222-2-2-2-222222222222-2-222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-2222222222-2-222-2-222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-20000000022-2-2-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2622222222-2-2-2-2-2-2-22222-20000000022-2-2-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2722222222-2-2-2-2-2-2-22222-200000000-2-22222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222222-2-2-2-2-2-2-22222-200000000-2-22222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ29222-2-2-2-2222-2-22-2-222-2-2222-2-222-2-20000000022-2-20000000000000000000000000000000000002i−2i2i−2i
χ30222-2-2-2-2222-2-22-2-222-2-2222-2-222-2-20000000022-2-2000000000000000000000000000000000000−2i2i−2i2i
χ31222-2-2-2-2222-2-22-2-222-2-22-2-222-2-22200000000-2-222000000000000000000000000000000002i−2i2i−2i0000
χ32222-2-2-2-2222-2-22-2-222-2-22-2-222-2-22200000000-2-22200000000000000000000000000000000−2i2i−2i2i0000
χ33222-2-2-2-22-2-2222-2-2-2-222222-2-222-2-200000000-2-222000000000000000000000000000000002-2-220000
χ34222-2-2-2-22-2-2222-2-2-2-222222-2-222-2-200000000-2-22200000000000000000000000000000000-222-20000
χ35222-2-2-2-22-2-2222-2-2-2-2222-2-222-2-2220000000022-2-20000000000000000000000000000000000002-2-22
χ36222-2-2-2-22-2-2222-2-2-2-2222-2-222-2-2220000000022-2-2000000000000000000000000000000000000-222-2
χ372-2-222-2-222-22-222-22-22-2-2000000000000000000002i2i−2i−2i2i2i−2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ382-2-222-2-222-22-222-22-22-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ392-2-222-2-222-22-222-22-22-2-200000000000000000000−2i−2i2i2i−2i−2i2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ402-2-222-2-222-22-222-22-22-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ412-2-222-2-222-22-2-2-22-22-2222222-2-2-2-2000000002-22-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ422-2-222-2-222-22-2-2-22-22-2222222-2-2-2-2000000002-22-200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ432-2-222-2-222-22-2-2-22-22-222-2-2-2-2222200000000-22-2200000000000000002-2-222-2-220000000000000000
χ442-2-222-2-222-22-2-2-22-22-222-2-2-2-2222200000000-22-220000000000000000-222-2-222-20000000000000000
χ452-2-222-2-22-22-2222-2-22-22-2000000000000000000002i2i−2i−2i−2i−2i2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ462-2-222-2-22-22-2222-2-22-22-2000000000000000000002i2i−2i−2i−2i−2i2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ472-2-222-2-22-22-2222-2-22-22-200000000000000000000−2i−2i2i2i2i2i−2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ482-2-222-2-22-22-2222-2-22-22-200000000000000000000−2i−2i2i2i2i2i−2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ492-2-222-2-22-22-22-2-222-22-222222-2-2-2-200000000-22-2200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ502-2-222-2-22-22-22-2-222-22-222222-2-2-2-200000000-22-220000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ512-2-222-2-22-22-22-2-222-22-22-2-2-2-22222000000002-22-2000000002-2-22-222-2000000000000000000000000
χ522-2-222-2-22-22-22-2-222-22-22-2-2-2-22222000000002-22-200000000-222-22-2-22000000000000000000000000
χ532-2-2-2-22222-2-22-22-2-222-2222-2-2-2-222000000002-2-22000000000000000000000000002-22-20000000000
χ542-2-2-2-22222-2-22-22-2-222-2222-2-2-2-222000000002-2-2200000000000000000000000000-22-220000000000
χ552-2-2-2-22222-2-22-22-2-222-22-2-22222-2-200000000-222-20000000000000000000000002-200002-200000000
χ562-2-2-2-22222-2-22-22-2-222-22-2-22222-2-200000000-222-2000000000000000000000000-220000-2200000000
χ572-2-2-2-2222-222-2-22-22-2-22222-2-2-2-22200000000-222-20000000000000000000000002-20000-2200000000
χ582-2-2-2-2222-222-2-22-22-2-22222-2-2-2-22200000000-222-2000000000000000000000000-2200002-200000000
χ592-2-2-2-2222-222-2-22-22-2-222-2-22222-2-2000000002-2-22000000000000000000000000002-2-220000000000
χ602-2-2-2-2222-222-2-22-22-2-222-2-22222-2-2000000002-2-2200000000000000000000000000-222-20000000000
χ61444-4-4-4-4444-4-4-444-4-444-4000000000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-4-444-44444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-40000000000002i2−2i22i2−2i22i2−2i22i2−2i20000004i−4i000022−2222−22000000000000000000000000000000000000
χ6444-44-44-4-40000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000−4i4i0000−2222−2222000000000000000000000000000000000000
χ6544-44-44-4-4000000000000−2i22i2−2i22i2−2i22i2−2i22i20000004i−4i0000−2222−2222000000000000000000000000000000000000
χ6644-44-44-4-4000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000−4i4i000022−2222−22000000000000000000000000000000000000
χ6744-4-44-44-40000000000002i2−2i2−2i22i22i2−2i2−2i22i200004i−4i000000000022−2222−2200000000000000000000000000000000
χ6844-4-44-44-40000000000002i2−2i2−2i22i22i2−2i2−2i22i20000−4i4i0000000000−2222−222200000000000000000000000000000000
χ6944-4-44-44-4000000000000−2i22i22i2−2i2−2i22i22i2−2i200004i−4i0000000000−2222−222200000000000000000000000000000000
χ7044-4-44-44-4000000000000−2i22i22i2−2i2−2i22i22i2−2i20000−4i4i000000000022−2222−2200000000000000000000000000000000
χ714-444-4-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i2004-4000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ724-444-4-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i200-4400000000−2i22i22i2−2i2000000000000000000000000000000000000
χ734-444-4-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i2004-400000000−2i22i22i2−2i2000000000000000000000000000000000000
χ744-444-4-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i200-44000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ754-44-444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i24-4000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ764-44-444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2-4400000000000000−2i22i22i2−2i200000000000000000000000000000000
χ774-44-444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i24-400000000000000−2i22i22i2−2i200000000000000000000000000000000
χ784-44-444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2-44000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ794-4-4-4-44444-4-444-444-4-44-4000000000000000000000000000000000000000000000000000000000000
χ804-4-4-4-4444-444-44-44-444-4-4000000000000000000000000000000000000000000000000000000000000

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