Finite Group Databasebeta

← Group #116403

Character table — Group #116403

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444444444444444488888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
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
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ91-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i1-111-1-1ii−i−i
χ101-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11−i−iii-11-1-111−i−iii
χ111-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii1-111-1-1−i−iii
χ121-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11ii−i−i-11-1-111ii−i−i
χ131-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1ii−i−i1-1-1-111−i−iii
χ141-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-11−i−iii-1111-1-1ii−i−i
χ151-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1−i−iii1-1-1-111ii−i−i
χ161-1-111-1-11-1-1111111-1-1111-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-11ii−i−i-1111-1-1−i−iii
χ17222222222222222222-2-2-2-2-2-222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ19222222222222-2-2-2-2-2-2222222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-222-2-22222-22-2-2-2-2-222-22-200000000000000000000000000000000000000002i−2i2i−2i0000
χ2422222222-2-2-2-222-2-22222-22-2-2-2-2-222-22-20000000000000000000000000000000000000000−2i2i−2i2i0000
χ2522222222-2-2-2-222-2-222-2-22-222-2-22-2-22-22000000000000000000000000000000000000000000002i−2i2i−2i
χ2622222222-2-2-2-222-2-222-2-22-222-2-22-2-22-2200000000000000000000000000000000000000000000−2i2i−2i2i
χ2722222222-2-2-2-2-2-222-2-222-22-2-222-22-22-2200000000000000000000000000000000220000-2-200000000
χ2822222222-2-2-2-2-2-222-2-222-22-2-222-22-22-2200000000000000000000000000000000-2-200002200000000
χ2922222222-2-2-2-2-2-222-2-2-2-22-222222-22-22-200000000000000000000000000000000002-22-20000000000
χ3022222222-2-2-2-2-2-222-2-2-2-22-222222-22-22-20000000000000000000000000000000000-22-220000000000
χ31222-2-2-2-222-22-20000002-22-22-200-22000000002i2i−2i−2i00002i2i−2i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−20000000000000000
χ32222-2-2-2-222-22-20000002-22-22-200-22000000002i2i−2i−2i00002i2i−2i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−220000000000000000
χ33222-2-2-2-222-22-20000002-22-22-200-2200000000−2i−2i2i2i0000−2i−2i2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−220000000000000000
χ34222-2-2-2-222-22-20000002-22-22-200-2200000000−2i−2i2i2i0000−2i−2i2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−20000000000000000
χ35222-2-2-2-222-22-2000000-22-22-22002-2000022-2-2000022-2-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ36222-2-2-2-222-22-2000000-22-22-22002-2000022-2-2000022-2-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ37222-2-2-2-222-22-2000000-22-22-22002-20000-2-2220000-2-2220000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ38222-2-2-2-222-22-2000000-22-22-22002-20000-2-2220000-2-2220000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ392-2-222-2-2222-2-222-2-2-2-222-2-22222-2-22-2-2200000000000000000000000000000000000000002i−2i−2i2i0000
χ402-2-222-2-2222-2-222-2-2-2-222-2-22222-2-22-2-220000000000000000000000000000000000000000−2i2i2i−2i0000
χ412-2-222-2-2222-2-222-2-2-2-2-2-222-2-22222-222-2000000000000000000000000000000000000000000002-2-22
χ422-2-222-2-2222-2-222-2-2-2-2-2-222-2-22222-222-200000000000000000000000000000000000000000000-222-2
χ432-2-222-2-2222-2-2-2-2222222-2-222-2-2-2-2-222-2000000000000000000000000000000002-20000-2200000000
χ442-2-222-2-2222-2-2-2-2222222-2-222-2-2-2-2-222-200000000000000000000000000000000-2200002-200000000
χ452-2-222-2-2222-2-2-2-22222-2-222-2-2-2-2222-2-2200000000000000000000000000000000002i−2i−2i2i0000000000
χ462-2-222-2-2222-2-2-2-22222-2-222-2-2-2-2222-2-220000000000000000000000000000000000−2i2i2i−2i0000000000
χ472-2-222-2-22-2-2222222-2-2-2-2-2222-2-2-22-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ482-2-222-2-22-2-2222222-2-2-2-2-2222-2-2-22-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ492-2-222-2-22-2-222-2-2-2-222222-2-2-2222-2-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ502-2-222-2-22-2-222-2-2-2-222222-2-2-2222-2-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ512-2-222-2-22-2-222-2-2-2-222-2-2-222222-2222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ522-2-222-2-22-2-222-2-2-2-222-2-2-222222-2222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ532-2-2-2-2222-222-20000002-222-2200-2-2000000002i2i−2i−2i0000−2i−2i2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ542-2-2-2-2222-222-20000002-222-2200-2-2000000002i2i−2i−2i0000−2i−2i2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ552-2-2-2-2222-222-20000002-222-2200-2-200000000−2i−2i2i2i00002i2i−2i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ562-2-2-2-2222-222-20000002-222-2200-2-200000000−2i−2i2i2i00002i2i−2i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ572-2-2-2-2222-222-2000000-22-2-22-20022000022-2-20000-2-22200002−2−22−222−22−2−22−222−20000000000000000
χ582-2-2-2-2222-222-2000000-22-2-22-20022000022-2-20000-2-2220000−222−22−2−22−222−22−2−220000000000000000
χ592-2-2-2-2222-222-2000000-22-2-22-200220000-2-222000022-2-200002−2−22−222−2−222−22−2−220000000000000000
χ602-2-2-2-2222-222-2000000-22-2-22-200220000-2-222000022-2-20000−222−22−2−222−2−22−222−20000000000000000
χ61444-4-4-4-44-44-440000004-4-4-4-4400440000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-44-44000000-44444-400-4-40000000000000000000000000000000000000000000000000000
χ6344-44-44-4-40000004-4000000004-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ6444-44-44-4-40000004-4000000004-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6544-44-44-4-4000000-4400000000-440000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6644-44-44-4-4000000-4400000000-44000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6744-4-44-44-400004i−4i004i−4i000000000000002i−2i−2i2i2-2-222i−2i−2i2i2-2-2200000000000000000000000000000000
χ6844-4-44-44-400004i−4i004i−4i00000000000000−2i2i2i−2i-222-2−2i2i2i−2i-222-200000000000000000000000000000000
χ6944-4-44-44-40000−4i4i00−4i4i000000000000002i−2i−2i2i-222-22i−2i−2i2i-222-200000000000000000000000000000000
χ7044-4-44-44-40000−4i4i00−4i4i00000000000000−2i2i2i−2i2-2-22−2i2i2i−2i2-2-2200000000000000000000000000000000
χ714-444-4-44-40000004-400000000-440000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ724-444-4-44-40000004-400000000-44000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ734-444-4-44-4000000-44000000004-40000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ744-444-4-44-4000000-44000000004-4000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ754-44-444-4-400004i−4i00−4i4i000000000000002i−2i−2i2i2-2-22−2i2i2i−2i-222-200000000000000000000000000000000
χ764-44-444-4-400004i−4i00−4i4i00000000000000−2i2i2i−2i-222-22i−2i−2i2i2-2-2200000000000000000000000000000000
χ774-44-444-4-40000−4i4i004i−4i000000000000002i−2i−2i2i-222-2−2i2i2i−2i2-2-2200000000000000000000000000000000
χ784-44-444-4-40000−4i4i004i−4i00000000000000−2i2i2i−2i2-2-222i−2i−2i2i-222-200000000000000000000000000000000
χ794-4-4-4-44444-4-440000004-4-444-4004-40000000000000000000000000000000000000000000000000000
χ804-4-4-4-44444-4-44000000-444-4-4400-440000000000000000000000000000000000000000000000000000

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