Finite Group Databasebeta

← Group #194112

Character table — Group #194112

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222244444444444444444444444444448888888888888888444444444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1111-1-1-1-1111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-111111-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ171-11-1-1-11111-1-111-111-1-11-1-111-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−ii−ii−iii−i−i11-1-111-1-111-1-111-1-11-11-1i−ii−i
χ181-11-1-1-11111-1-111-111-1-11-1-111-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iiii−ii−i−i−iii-1-111-1-11111-1-111-1-1-11-11−ii−ii
χ191-11-1-1-11111-1-111-111-1-11-1-111-1-1-11ii−i−iii−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−ii−ii−iii−i−i11-1-111-1-1-1-111-1-111-11-11−ii−ii
χ201-11-1-1-11111-1-111-111-1-11-1-111-1-1-11ii−i−iii−i−i11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iiii−ii−i−i−iii-1-111-1-111-1-111-1-1111-11-1i−ii−i
χ211-11-1-1-11111-1-111-111-1-11-1-111-1-1-11−i−iii−i−iii11-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i−ii−iiii−i−i-1-111-1-111-1-111-1-1111-11-1−ii−ii
χ221-11-1-1-11111-1-111-111-1-11-1-111-1-1-11−i−iii−i−iii11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−ii−ii−i−iii11-1-111-1-1-1-111-1-111-11-11i−ii−i
χ231-11-1-1-11111-1-111-111-1-11-1-111-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i−ii−iiii−i−i-1-111-1-11111-1-111-1-1-11-11i−ii−i
χ241-11-1-1-11111-1-111-111-1-11-1-111-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−ii−ii−i−iii11-1-111-1-111-1-111-1-11-11-1−ii−ii
χ251-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11ii−i−i−i−iii1-11-1iiii−i−i−i−i−i−i−i−iiiiiii−i−ii−i−ii−i−iii11-1-1-1-11111-1-1-1-1111-1-11i−i−ii
χ261-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11ii−i−i−i−iii1-11-1iiii−i−i−i−i−i−i−i−iiiii−i−iiii−i−iiii−i−i-1-11111-1-111-1-1-1-111-111-1−iii−i
χ271-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11ii−i−i−i−iii1-11-1−i−i−i−iiiiiiiii−i−i−i−iii−i−ii−i−ii−i−iii11-1-1-1-111-1-11111-1-1-111-1−iii−i
χ281-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11ii−i−i−i−iii1-11-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiii−i−iiii−i−i-1-11111-1-1-1-11111-1-11-1-11i−i−ii
χ291-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11−i−iiiii−i−i1-11-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−iii−i−i−iii-1-11111-1-1-1-11111-1-11-1-11−iii−i
χ301-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11−i−iiiii−i−i1-11-1iiii−i−i−i−i−i−i−i−iiiii−i−iii−iii−iii−i−i11-1-1-1-111-1-11111-1-1-111-1i−i−ii
χ311-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11−i−iiiii−i−i1-11-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−iii−i−i−iii-1-11111-1-111-1-1-1-111-111-1i−i−ii
χ321-11-1-1-111-1-11111-1-1-1111-1-1-1-111-11−i−iiiii−i−i1-11-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii−iii−iii−i−i11-1-1-1-11111-1-1-1-1111-1-11−iii−i
χ332222222222222222222-2-2-2-2-2-2-22-222222222-2-2-2-200000000000000000000-2-2-2-20000000000000000000000000000
χ342222222222222222222-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-22222222-2200000000-2-2-2-200000000000000000000000000002-22-22-22-20000000000000000
χ36222222222222-2-2-2-2-2-2-22222222-2200000000-2-2-2-20000000000000000000000000000-22-22-22-220000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000002-22-200002-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-22-220000-22-22000000000000000000000000
χ3922222222-2-2-2-2222-2-2-2-2-2-2-222222-22222-2-2-2-2-222-200000000000000000000-2-2220000000000000000000000000000
χ4022222222-2-2-2-2222-2-2-2-2-2-2-222222-2-2-2-2-22222-222-20000000000000000000022-2-20000000000000000000000000000
χ4122222222-2-2-2-2-2-2-22222222-2-2-2-2-2200000000-222-200000000000000000000000000002-22-2-22-220000000000000000
χ4222222222-2-2-2-2-2-2-22222222-2-2-2-2-2200000000-222-20000000000000000000000000000-22-222-22-20000000000000000
χ4322222222-2-2-2-2-2-2-22222-2-2-22222-2-2000000002-2-2200000000000000002-22-20000-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-22222-2-2-22222-2-2000000002-2-220000000000000000-22-2200002-22-2000000000000000000000000
χ452222-2-2-2-22-22-22-222-22-20000000-202-22-22-22-2000022−2−222−2−222−2−222−2−2000000000000000000002−22−22−22−200000000
χ462222-2-2-2-22-22-22-222-22-20000000-202-22-22-22-20000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ472222-2-2-2-22-22-22-222-22-20000000-20-22-22-22-22000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ482222-2-2-2-22-22-22-222-22-20000000-20-22-22-22-220000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
χ492222-2-2-2-2-22-222-22-22-220000000-202-22-2-22-22000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ502222-2-2-2-2-22-222-22-22-220000000-202-22-2-22-220000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ512222-2-2-2-2-22-222-22-22-220000000-20-22-222-22-2000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ522222-2-2-2-2-22-222-22-22-220000000-20-22-222-22-20000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ532-22-222-2-22-2-222-2-22-2-220000000202i−2i−2i2i2i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−222−2−2200000000
χ542-22-222-2-22-2-222-2-22-2-220000000202i−2i−2i2i2i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−222−200000000
χ552-22-222-2-22-2-222-2-22-2-22000000020−2i2i2i−2i−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−222−200000000
χ562-22-222-2-22-2-222-2-22-2-22000000020−2i2i2i−2i−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−222−2−2200000000
χ572-22-222-2-2-222-22-2-2-222-20000000202i−2i−2i2i−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−222−200000000
χ582-22-222-2-2-222-22-2-2-222-20000000202i−2i−2i2i−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−22−2−2200000000
χ592-22-222-2-2-222-22-2-2-222-2000000020−2i2i2i−2i2i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−22−2−2200000000
χ602-22-222-2-2-222-22-2-2-222-2000000020−2i2i2i−2i2i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−222−200000000
χ612-22-2-2-22222-2-222-222-2-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i-2-22200000000000000000000−2i2i−2i2i0000000000000000000000000000
χ622-22-2-2-22222-2-222-222-2-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000002i−2i2i−2i0000000000000000000000000000
χ632-22-2-2-22222-2-2-2-22-2-2222-2-222-2-22200000000-2-22200000000000000000000000000002-2-222-2-220000000000000000
χ642-22-2-2-22222-2-2-2-22-2-2222-2-222-2-22200000000-2-2220000000000000000000000000000-222-2-222-20000000000000000
χ652-22-2-2-22222-2-2-2-22-2-222-222-2-2222-20000000022-2-200000000000000002i−2i−2i2i00002i−2i−2i2i000000000000000000000000
χ662-22-2-2-22222-2-2-2-22-2-222-222-2-2222-20000000022-2-20000000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000000000000000
χ672-22-2-2-222-2-22222-2-2-222-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i-22-2200000000000000000000−2i2i2i−2i0000000000000000000000000000
χ682-22-2-2-222-2-22222-2-2-222-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-22-22000000000000000000002i−2i−2i2i0000000000000000000000000000
χ692-22-2-2-222-2-222-2-2222-2-22-2-2-2-2222200000000-22-2200000000000000000000000000002-2-22-222-20000000000000000
χ702-22-2-2-222-2-222-2-2222-2-22-2-2-2-2222200000000-22-220000000000000000000000000000-222-22-2-220000000000000000
χ712-22-2-2-222-2-222-2-2222-2-2-22222-2-22-2000000002-22-200000000000000002i−2i−2i2i0000−2i2i2i−2i000000000000000000000000
χ722-22-2-2-222-2-222-2-2222-2-2-22222-2-22-2000000002-22-20000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000000000000000
χ734444-4-4-4-44-44-4-44-4-44-440000000400000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-44-44-44-44-44-40000000400000000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-44-40000000000044-400000-40000000000000000000022−2222−2222−2222−22000000000000000000000000000000000000
χ7644-4-44-44-40000000000044-400000-400000000000000000000−2222−2222−2222−2222000000000000000000000000000000000000
χ7744-4-44-44-400000000000-4-440000040000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ7844-4-44-44-400000000000-4-44000004000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ7944-4-4-44-44000000000000004i−4i4i−4i000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000000000
χ8044-4-4-44-44000000000000004i−4i4i−4i00000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000000000
χ8144-4-4-44-4400000000000000−4i4i−4i4i000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000000000
χ8244-4-4-44-4400000000000000−4i4i−4i4i00000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000000000
χ834-44-444-4-44-4-44-444-444-40000000-400000000000000000000000000000000000000000000000000000000000000000
χ844-44-444-4-4-444-4-4444-4-440000000-400000000000000000000000000000000000000000000000000000000000000000
χ854-4-444-4-44000000000000004i−4i−4i4i000000000000002-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ864-4-444-4-44000000000000004i−4i−4i4i00000000000000-222-22-2-222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ874-4-444-4-4400000000000000−4i4i4i−4i000000000000002-2-22-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ884-4-444-4-4400000000000000−4i4i4i−4i00000000000000-222-22-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ894-4-44-444-4000000000004-4400000-4000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ904-4-44-444-4000000000004-4400000-400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ914-4-44-444-400000000000-44-400000400000000000022−2222−22−2222−222200000000000000000000000000000000000000000000
χ924-4-44-444-400000000000-44-4000004000000000000−2222−222222−2222−2200000000000000000000000000000000000000000000

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