Finite Group Databasebeta

← Group #384159

Character table — Group #384159

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222444444444444444444444444888888888888888888888888161616161616161616161616
order12222222222244444444444444448888888888888888222222444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-11111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-11111-1-1-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111111111-1-1-1-111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111111111-1-1
χ171-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-11-1i−ii−i11-1-11-1i−ii−ii−ii−i1-1i−i1-1i−i
χ181-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-11-11-11−ii−ii11-1-1-11−ii−iii−ii−i-11−ii-11−ii
χ191-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-111-1i−i−ii-1-111-11i−i−ii−ii−ii1-1i−i-11−ii
χ201-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-111-1-11−iii−i-1-1111-1−iii−i−ii−ii-11−ii1-1i−i
χ211-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-11-1−ii−ii11-1-11-1−ii−ii−ii−ii1-1−ii1-1−ii
χ221-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-11-11i−ii−i11-1-1-11i−ii−i−ii−ii-11i−i-11i−i
χ231-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-111-1−iii−i-1-111-11−iii−ii−ii−i1-1−ii-11i−i
χ241-111-1-11-11-1-1111-111-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-111-1-11i−i−ii-1-1111-1i−i−iii−ii−i-11i−i1-1−ii
χ251-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-11-1-111-1−ii−ii-1-111-11−ii−ii−iii−i-11i−i1-1i−i
χ261-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-111-1-11i−ii−i-1-1111-1i−ii−i−iii−i1-1−ii-11−ii
χ271-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1111-11-11-1−iii−i11-1-11-1−iii−ii−i−ii-11i−i-11−ii
χ281-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-11-11-11i−i−ii11-1-1-11i−i−iii−i−ii1-1−ii1-1i−i
χ291-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-11-1-111-1i−ii−i-1-111-11i−ii−ii−i−ii-11−ii1-1−ii
χ301-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-111-1-11−ii−ii-1-1111-1−ii−iii−i−ii1-1i−i-11i−i
χ311-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-11-11-1i−i−ii11-1-11-1i−i−ii−iii−i-11−ii-11i−i
χ321-111-1-11-11-1-1111-111-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-11-11−iii−i11-1-1-11−iii−i−iii−i1-1i−i1-1−ii
χ3322222222-2-2-2-22-222-2-2-22000000000000000022-2-222-2-200002200-2-22200000000-2-200000000000000
χ3422222222-2-2-2-22-222-2-2-22000000000000000022-2-222-2-20000-2-20022-2-2000000002200000000000000
χ3522222222-2-2-2-22-222-2-2-220000000000000000-2-222-2-22200002200-2-2-2-2000000002200000000000000
χ3622222222-2-2-2-22-222-2-2-220000000000000000-2-222-2-2220000-2-200222200000000-2-200000000000000
χ3722222222-2-2-2-2-22-2-2222-20000000022-2-222-2-200000000000000220000220000-2-200-2-2000000000000
χ3822222222-2-2-2-2-22-2-2222-20000000022-2-222-2-200000000000000-2-20000-2-20000220022000000000000
χ3922222222-2-2-2-2-22-2-2222-200000000-2-222-2-22200000000000000220000-2-20000-2-20022000000000000
χ4022222222-2-2-2-2-22-2-2222-200000000-2-222-2-22200000000000000-2-200002200002200-2-2000000000000
χ4122-222-2-2-222-2-2-22-22-22-222i2i−2i−2i2i2i−2i−2i00000000000000002-22-200000000002i−2i2i−2i000000000000000000
χ4222-222-2-2-222-2-2-22-22-22-222i2i−2i−2i2i2i−2i−2i0000000000000000-22-220000000000−2i2i−2i2i000000000000000000
χ4322-222-2-2-222-2-2-22-22-22-22−2i−2i2i2i−2i−2i2i2i00000000000000002-22-20000000000−2i2i−2i2i000000000000000000
χ4422-222-2-2-222-2-2-22-22-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000-22-2200000000002i−2i2i−2i000000000000000000
χ452-222-2-22-2-222-22-2-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i00002-200-222i−2i00000000−2i2i00000000000000
χ462-222-2-22-2-222-22-2-22-222-200000000000000002i2i−2i−2i−2i−2i2i2i0000-22002-2−2i2i000000002i−2i00000000000000
χ472-222-2-22-2-222-22-2-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i00002-200-22−2i2i000000002i−2i00000000000000
χ482-222-2-22-2-222-22-2-22-222-20000000000000000−2i−2i2i2i2i2i−2i−2i0000-22002-22i−2i00000000−2i2i00000000000000
χ492-222-2-22-2-222-2-222-22-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000002-200002i−2i0000-2200−2i2i000000000000
χ502-222-2-22-2-222-2-222-22-2-22000000002i2i−2i−2i−2i−2i2i2i00000000000000-220000−2i2i00002-2002i−2i000000000000
χ512-222-2-22-2-222-2-222-22-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000002-20000−2i2i0000-22002i−2i000000000000
χ522-222-2-22-2-222-2-222-22-2-2200000000−2i−2i2i2i2i2i−2i−2i00000000000000-2200002i−2i00002-200−2i2i000000000000
χ532-2-22-22-222-22-2-2222-2-22-22i2i−2i−2i−2i−2i2i2i00000000000000002-2-2200000000002i−2i−2i2i000000000000000000
χ542-2-22-22-222-22-2-2222-2-22-22i2i−2i−2i−2i−2i2i2i0000000000000000-222-20000000000−2i2i2i−2i000000000000000000
χ552-2-22-22-222-22-2-2222-2-22-2−2i−2i2i2i2i2i−2i−2i00000000000000002-2-220000000000−2i2i2i−2i000000000000000000
χ562-2-22-22-222-22-2-2222-2-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000-222-200000000002i−2i−2i2i000000000000000000
χ57444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ58444-4-4-4-440000000000002i−2i2i−2i2i−2i2i−2i0022−220022−222i2−2i2002i2−2i200000000000000000000000000000000000000
χ59444-4-4-4-440000000000002i−2i2i−2i2i−2i2i−2i00−222200−2222−2i22i200−2i22i200000000000000000000000000000000000000
χ60444-4-4-4-44000000000000−2i2i−2i2i−2i2i−2i2i0022−220022−22−2i22i200−2i22i200000000000000000000000000000000000000
χ61444-4-4-4-44000000000000−2i2i−2i2i−2i2i−2i2i00−222200−22222i2−2i2002i2−2i200000000000000000000000000000000000000
χ6244-444-4-4-444-4-44-44-44-44-4000000000000000000000000000000000000000000000000000000000000
χ6344-444-4-4-4-4-444444-4-44-4-4000000000000000000000000000000000000000000000000000000000000
χ6444-444-4-4-4-4-444-4-4-444-444000000000000000000000000000000000000000000000000000000000000
χ6544-4-4-444-40000000000002-2-222-2-222i2−2i2002i2−2i200002i2−2i2002i2−2i2000000000000000000000000000000000000
χ6644-4-4-444-40000000000002-2-222-2-22−2i22i200−2i22i20000−2i22i200−2i22i2000000000000000000000000000000000000
χ6744-4-4-444-4000000000000-222-2-222-22i2−2i2002i2−2i20000−2i22i200−2i22i2000000000000000000000000000000000000
χ6844-4-4-444-4000000000000-222-2-222-2−2i22i200−2i22i200002i2−2i2002i2−2i2000000000000000000000000000000000000
χ694-444-4-44-44-4-44-4-44-4-4444000000000000000000000000000000000000000000000000000000000000
χ704-44-444-4-40000000000002i−2i2i−2i−2i2i−2i2i002i2−2i200−2i22i2−22220022−2200000000000000000000000000000000000000
χ714-44-444-4-40000000000002i−2i2i−2i−2i2i−2i2i00−2i22i2002i2−2i222−2200−222200000000000000000000000000000000000000
χ724-44-444-4-4000000000000−2i2i−2i2i2i−2i2i−2i002i2−2i200−2i22i222−2200−222200000000000000000000000000000000000000
χ734-44-444-4-4000000000000−2i2i−2i2i2i−2i2i−2i00−2i22i2002i2−2i2−22220022−2200000000000000000000000000000000000000
χ744-4-44-44-444-44-44-4-4-444-44000000000000000000000000000000000000000000000000000000000000
χ754-4-44-44-44-44-4444-4-4-4-444000000000000000000000000000000000000000000000000000000000000
χ764-4-44-44-44-44-44-4-44444-4-4000000000000000000000000000000000000000000000000000000000000
χ774-4-4-44-4440000000000002-2-22-222-222−2200−2222000022−2200−2222000000000000000000000000000000000000
χ784-4-4-44-4440000000000002-2-22-222-2−22220022−220000−22220022−22000000000000000000000000000000000000
χ794-4-4-44-444000000000000-222-22-2-2222−2200−22220000−22220022−22000000000000000000000000000000000000
χ804-4-4-44-444000000000000-222-22-2-22−22220022−22000022−2200−2222000000000000000000000000000000000000

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