Finite Group Databasebeta

← Group #229358

Character table — Group #229358

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888844444444448888888888888888884444444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ31111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111111111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ7111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ911111111111111111-1-1-1-1111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111
χ1111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1211111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ1311111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ1411111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ1511111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111
χ171-11-11-11-1-111-1-1-1111ii−i−iii−i−iii−i−i-111-1-1iiii−i−i−i−ii−i1-1i−i1-1i−iii−i−i1-111-1-111-1-1ii−i−i1-1i−i1-1i−i1-1
χ181-11-11-11-1-111-1-1-1111ii−i−iii−i−iii−i−i-111-1-1−i−i−i−iiiiii−i-11i−i-11i−iii−i−i1-1-1-111-1-111−i−iii1-1−ii1-1−ii-11
χ191-11-11-11-1-111-1-1-1111ii−i−iii−i−i−i−iii-111-1-1iiii−i−i−i−ii−i-11−ii-11i−i−i−iii1-111-1-111-1-1ii−i−i-11−ii-11−ii-11
χ201-11-11-11-1-111-1-1-1111ii−i−iii−i−i−i−iii-111-1-1−i−i−i−iiiiii−i1-1−ii1-1i−i−i−iii1-1-1-111-1-111−i−iii-11i−i-11i−i1-1
χ211-11-11-11-1-111-1-1-1111ii−i−i−i−iiiii−i−i-1-1-111iiii−i−i−i−ii−i1-1i−i1-1−ii−i−iii-1111-1-1-1-111−i−iii1-1i−i-11−ii-11
χ221-11-11-11-1-111-1-1-1111ii−i−i−i−iiiii−i−i-1-1-111−i−i−i−iiiiii−i-11i−i-11−ii−i−iii-11-1-11111-1-1ii−i−i1-1−ii-11i−i1-1
χ231-11-11-11-1-111-1-1-1111ii−i−i−i−iii−i−iii-1-1-111iiii−i−i−i−ii−i-11−ii-11−iiii−i−i-1111-1-1-1-111−i−iii-11−ii1-1i−i1-1
χ241-11-11-11-1-111-1-1-1111ii−i−i−i−iii−i−iii-1-1-111−i−i−i−iiiiii−i1-1−ii1-1−iiii−i−i-11-1-11111-1-1ii−i−i-11i−i1-1−ii-11
χ251-11-11-11-1-111-1-1-1111−i−iiiii−i−iii−i−i-1-1-111iiii−i−i−i−i−ii1-1i−i1-1i−i−i−iii-11-1-11111-1-1−i−iii-11−ii1-1i−i-11
χ261-11-11-11-1-111-1-1-1111−i−iiiii−i−iii−i−i-1-1-111−i−i−i−iiiii−ii-11i−i-11i−i−i−iii-1111-1-1-1-111ii−i−i-11i−i1-1−ii1-1
χ271-11-11-11-1-111-1-1-1111−i−iiiii−i−i−i−iii-1-1-111iiii−i−i−i−i−ii-11−ii-11i−iii−i−i-11-1-11111-1-1−i−iii1-1i−i-11−ii1-1
χ281-11-11-11-1-111-1-1-1111−i−iiiii−i−i−i−iii-1-1-111−i−i−i−iiiii−ii1-1−ii1-1i−iii−i−i-1111-1-1-1-111ii−i−i1-1−ii-11i−i-11
χ291-11-11-11-1-111-1-1-1111−i−iii−i−iiiii−i−i-111-1-1iiii−i−i−i−i−ii1-1i−i1-1−iiii−i−i1-1-1-111-1-111ii−i−i-11−ii-11−ii1-1
χ301-11-11-11-1-111-1-1-1111−i−iii−i−iiiii−i−i-111-1-1−i−i−i−iiiii−ii-11i−i-11−iiii−i−i1-111-1-111-1-1−i−iii-11i−i-11i−i-11
χ311-11-11-11-1-111-1-1-1111−i−iii−i−iii−i−iii-111-1-1iiii−i−i−i−i−ii-11−ii-11−ii−i−iii1-1-1-111-1-111ii−i−i1-1i−i1-1i−i-11
χ321-11-11-11-1-111-1-1-1111−i−iii−i−iii−i−iii-111-1-1−i−i−i−iiiii−ii1-1−ii1-1−ii−i−iii1-111-1-111-1-1−i−iii1-1−ii1-1−ii1-1
χ33222222222-22-2-222-2-2222222220000-2222200000000-2-2000000-2-20000-2-20000000000000000000000
χ34222222222-22-2-222-2-22222-2-2-2-20000-2-2-2-2-200000000-2-2000000220000220000000000000000000000
χ35222222222-22-2-222-2-2-2-2-2-222220000-2-2-2-2-20000000022000000-2-20000220000000000000000000000
χ36222222222-22-2-222-2-2-2-2-2-2-2-2-2-20000-222220000000022000000220000-2-20000000000000000000000
χ3722222222-22-222-2-22-2000000002222-2000022-2-222-2-20022-2-2-2-2000000000000000000000000000000
χ3822222222-22-222-2-22-2000000002222-20000-2-222-2-22200-2-2-2-222000000000000000000000000000000
χ3922222222-22-222-2-22-200000000-2-2-2-2-2000022-2-222-2-200-2-22222000000000000000000000000000000
χ4022222222-22-222-2-22-200000000-2-2-2-2-20000-2-222-2-222002222-2-2000000000000000000000000000000
χ4122-2-222-2-2-20-20022002i−2i2i−2i2-22-2000002i−2i2i−2i2−22−22−22−20000000000000000i2−i2i2−i22−22−2i2−i2i2−i20000000000
χ4222-2-222-2-2-20-20022002i−2i2i−2i2-22-2000002i−2i2i−2i−22−22−22−220000000000000000−i2i2−i2i2−22−22−i2i2−i2i20000000000
χ4322-2-222-2-2-20-20022002i−2i2i−2i-22-2200000−2i2i−2i2i2−22−22−22−20000000000000000i2−i2i2−i2−22−22−i2i2−i2i20000000000
χ4422-2-222-2-2-20-20022002i−2i2i−2i-22-2200000−2i2i−2i2i−22−22−22−220000000000000000−i2i2−i2i22−22−2i2−i2i2−i20000000000
χ4522-2-222-2-2-20-2002200−2i2i−2i2i2-22-200000−2i2i−2i2i2−22−22−22−20000000000000000−i2i2−i2i22−22−2−i2i2−i2i20000000000
χ4622-2-222-2-2-20-2002200−2i2i−2i2i2-22-200000−2i2i−2i2i−22−22−22−220000000000000000i2−i2i2−i2−22−22i2−i2i2−i20000000000
χ4722-2-222-2-2-20-2002200−2i2i−2i2i-22-22000002i−2i2i−2i2−22−22−22−20000000000000000−i2i2−i2i2−22−22i2−i2i2−i20000000000
χ4822-2-222-2-2-20-2002200−2i2i−2i2i-22-22000002i−2i2i−2i−22−22−22−220000000000000000i2−i2i2−i22−22−2−i2i2−i2i20000000000
χ492-22-22-22-222-2-2-22-22-2000000002i2i−2i−2i200002i2i−2i−2i−2i−2i2i2i002-2−2i2i-22000000000000000000000000000000
χ502-22-22-22-222-2-2-22-22-2000000002i2i−2i−2i20000−2i−2i2i2i2i2i−2i−2i00-22−2i2i2-2000000000000000000000000000000
χ512-22-22-22-222-2-2-22-22-200000000−2i−2i2i2i200002i2i−2i−2i−2i−2i2i2i00-222i−2i2-2000000000000000000000000000000
χ522-22-22-22-222-2-2-22-22-200000000−2i−2i2i2i20000−2i−2i2i2i2i2i−2i−2i002-22i−2i-22000000000000000000000000000000
χ532-22-22-22-2-2-2222-22-2-22i2i−2i−2i2i2i−2i−2i0000222-2-200000000−2i2i000000−2i2i0000-220000000000000000000000
χ542-22-22-22-2-2-2222-22-2-22i2i−2i−2i−2i−2i2i2i00002-2-22200000000−2i2i0000002i−2i00002-20000000000000000000000
χ552-22-22-22-2-2-2222-22-2-2−2i−2i2i2i2i2i−2i−2i00002-2-222000000002i−2i000000−2i2i00002-20000000000000000000000
χ562-22-22-22-2-2-2222-22-2-2−2i−2i2i2i−2i−2i2i2i0000222-2-2000000002i−2i0000002i−2i0000-220000000000000000000000
χ572-2-222-2-2220-200-22002-2-222i−2i−2i2i00000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i22−2−222−2−220000000000
χ582-2-222-2-2220-200-22002-2-222i−2i−2i2i00000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i2−222−2−222−20000000000
χ592-2-222-2-2220-200-22002-2-22−2i2i2i−2i000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i2−222−2−222−20000000000
χ602-2-222-2-2220-200-22002-2-22−2i2i2i−2i000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i22−2−222−2−220000000000
χ612-2-222-2-2220-200-2200-222-22i−2i−2i2i000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i22−2−22−222−20000000000
χ622-2-222-2-2220-200-2200-222-22i−2i−2i2i000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i2−222−22−2−220000000000
χ632-2-222-2-2220-200-2200-222-2−2i2i2i−2i00000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i2−222−22−2−220000000000
χ642-2-222-2-2220-200-2200-222-2−2i2i2i−2i00000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i22−2−22−222−20000000000
χ6544444444-4-4-4-4-4-4-4-44000000000000400000000000000000000000000000000000000000000000000
χ6644-44-4-44-40404-400-400000000000000000000000000000000000022−2222−22000000000000000000000000
χ6744-44-4-44-40404-400-4000000000000000000000000000000000000−2222−2222000000000000000000000000
χ6844-44-4-44-40-40-440040000000004i−4i4i−4i000000000000000000000000000000000000000000000000000
χ6944-44-4-44-40-40-44004000000000−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ7044-4-444-4-440400-4-4000000000000000000022−22−222222−22−222200000000000000000000000000000000000000
χ7144-4-444-4-440400-4-40000000000000000000−222222−22−222222−2200000000000000000000000000000000000000
χ724-44-44-44-44-4-4444-4-44000000000000-400000000000000000000000000000000000000000000000000
χ734-4-444-4-44-404004-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ744-4-444-4-44-404004-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ754-4-4-4-4444040-4400-40000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ764-4-4-4-4444040-4400-4000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ774-4-4-4-44440-404-40040000000004-4-44000000000000000000000000000000000000000000000000000
χ784-4-4-4-44440-404-4004000000000-444-4000000000000000000000000000000000000000000000000000
χ79888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000
χ808-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000

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