Finite Group Databasebeta

← Group #307405

Character table — Group #307405

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-11-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-11-111-1-111-1-1-11
χ1722222222222-2-2-2-2200000000-22222-200002222-2-2-2-20000000000-2-22200-2-200000000000000000000
χ1822222222222-2-2-2-2200000000-22222-20000-2-2-2-222220000000000-2-2-2-2002200000000000000000000
χ1922222222222-2-2-2-2200000000-2-2-2-2-2-200002222-2-2-2-2000000000022-2-2002200000000000000000000
χ2022222222222-2-2-2-2200000000-2-2-2-2-2-20000-2-2-2-222220000000000222200-2-200000000000000000000
χ2122222222-2-2-22222-222222222-20000-2-2-2-2-20000000000000000220000220000000000-2-20000000000
χ2222222222-2-2-22222-222222222-20000-2-2-2-2-20000000000000000-2-20000-2-20000000000220000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-2-20000-222220000000000000000220000-2-200000000002-20000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2-20000-222220000000000000000-2-20000220000000000-220000000000
χ252222-2-2-2-2-22-2000022222−2−2−2−202i2i−2i−2i022−2−2000022-2-22222−2−2−2−2000000002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ262222-2-2-2-2-22-2000022222−2−2−2−202i2i−2i−2i022−2−20000-2-222−2−2−2−2222200000000−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ272222-2-2-2-2-22-2000022222−2−2−2−20−2i−2i2i2i022−2−2000022-2-22222−2−2−2−200000000−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ282222-2-2-2-2-22-2000022222−2−2−2−20−2i−2i2i2i022−2−20000-2-222−2−2−2−22222000000002i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ292222-2-2-2-2-22-200002−2−2−2−2222202i2i−2i−2i0−2−222000022-2-2−2−2−2−22222000000002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ302222-2-2-2-2-22-200002−2−2−2−2222202i2i−2i−2i0−2−2220000-2-2222222−2−2−2−200000000−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ312222-2-2-2-2-22-200002−2−2−2−222220−2i−2i2i2i0−2−222000022-2-2−2−2−2−2222200000000−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ322222-2-2-2-2-22-200002−2−2−2−222220−2i−2i2i2i0−2−2220000-2-2222222−2−2−2−2000000002i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ3322-2-22-22-20002-22-202i2i−2i−2i2i2i−2i−2i0000000000i2i2−i2−i2i2−i2i2−i222−2−222−2−22-200002i−2i0000000000000000i2−i22−200
χ3422-2-22-22-20002-22-202i2i−2i−2i2i2i−2i−2i0000000000i2i2−i2−i2i2−i2i2−i222−2−222−2−2-220000−2i2i0000000000000000−i2i2−2200
χ3522-2-22-22-20002-22-202i2i−2i−2i2i2i−2i−2i0000000000−i2−i2i2i2−i2i2−i2i2−2−222−2−2222-200002i−2i0000000000000000−i2i2−2200
χ3622-2-22-22-20002-22-202i2i−2i−2i2i2i−2i−2i0000000000−i2−i2i2i2−i2i2−i2i2−2−222−2−222-220000−2i2i0000000000000000i2−i22−200
χ3722-2-22-22-20002-22-20−2i−2i2i2i−2i−2i2i2i0000000000i2i2−i2−i2i2−i2i2−i2−2−222−2−2222-20000−2i2i0000000000000000i2−i2−2200
χ3822-2-22-22-20002-22-20−2i−2i2i2i−2i−2i2i2i0000000000i2i2−i2−i2i2−i2i2−i2−2−222−2−222-2200002i−2i0000000000000000−i2i22−200
χ3922-2-22-22-20002-22-20−2i−2i2i2i−2i−2i2i2i0000000000−i2−i2i2i2−i2i2−i2i222−2−222−2−22-20000−2i2i0000000000000000−i2i22−200
χ4022-2-22-22-20002-22-20−2i−2i2i2i−2i−2i2i2i0000000000−i2−i2i2i2−i2i2−i2i222−2−222−2−2-2200002i−2i0000000000000000i2−i2−2200
χ412-2-2222-2-22-2-222-2-222-22-22-22-220000-22-22-20000000000000000000000000000000000002i−2i2i−2i000000
χ422-2-2222-2-22-2-222-2-222-22-22-22-220000-22-22-2000000000000000000000000000000000000−2i2i−2i2i000000
χ432-2-2222-2-22-2-222-2-22-22-22-22-2220000-2-22-220000000000000000000000000000000000002i−2i−2i2i000000
χ442-2-2222-2-22-2-222-2-22-22-22-22-2220000-2-22-22000000000000000000000000000000000000−2i2i2i−2i000000
χ452-2-2222-2-2-22222-2-2-22-22-22-22-2-22i−2i2i−2i2-22-220000000000000000002i−2i0000002i−2i2i−2i0000000000000000
χ462-2-2222-2-2-22222-2-2-22-22-22-22-2-2−2i2i−2i2i2-22-22000000000000000000−2i2i000000−2i2i−2i2i0000000000000000
χ472-2-2222-2-2-22222-2-2-2-22-22-22-22-22i−2i2i−2i22-22-20000000000000000002i−2i000000−2i2i−2i2i0000000000000000
χ482-2-2222-2-2-22222-2-2-2-22-22-22-22-2−2i2i−2i2i22-22-2000000000000000000−2i2i0000002i−2i2i−2i0000000000000000
χ492-2-2222-2-2-222-2-222-20000000022i−2i2i−2i-20000000000002i−2i2i−2i2i−2i2i−2i00−2i2i00000000002-22-2000000000000
χ502-2-2222-2-2-222-2-222-20000000022i−2i2i−2i-2000000000000−2i2i−2i2i−2i2i−2i2i00−2i2i0000000000-22-22000000000000
χ512-2-2222-2-2-222-2-222-2000000002−2i2i−2i2i-20000000000002i−2i2i−2i2i−2i2i−2i002i−2i0000000000-22-22000000000000
χ522-2-2222-2-2-222-2-222-2000000002−2i2i−2i2i-2000000000000−2i2i−2i2i−2i2i−2i2i002i−2i00000000002-22-2000000000000
χ532-2-22-2-22222-20000-22−22−2−22−2202-2-220−222−22i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i200002i−2i00002−2−22−i2i2i2−i2000000000000
χ542-2-22-2-22222-20000-22−22−2−22−2202-2-220−222−2−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i20000−2i2i00002−2−22i2−i2−i2i2000000000000
χ552-2-22-2-22222-20000-22−22−2−22−220-222-20−222−22i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i20000−2i2i0000−222−2i2−i2−i2i2000000000000
χ562-2-22-2-22222-20000-22−22−2−22−220-222-20−222−2−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i200002i−2i0000−222−2−i2i2i2−i2000000000000
χ572-2-22-2-22222-20000-2−22−222−22−202-2-2202−2−222i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i200002i−2i0000−222−2i2−i2−i2i2000000000000
χ582-2-22-2-22222-20000-2−22−222−22−202-2-2202−2−22−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i20000−2i2i0000−222−2−i2i2i2−i2000000000000
χ592-2-22-2-22222-20000-2−22−222−22−20-222-202−2−222i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i20000−2i2i00002−2−22−i2i2i2−i2000000000000
χ602-2-22-2-22222-20000-2−22−222−22−20-222-202−2−22−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i200002i−2i00002−2−22i2−i2−i2i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ624444-4-4-4-44-440000-422222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ634444-4-4-4-44-440000-4−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-4-44-44-4000-44-4400000000000000000002i22i2−2i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ6544-4-44-44-4000-44-440000000000000000000−2i2−2i22i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ6644-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000002i2−2i2−2i22i222-2-2-2-222000000000000000000000000000000
χ6744-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000−2i22i22i2−2i2-2-22222-2-2000000000000000000000000000000
χ6844-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000002i2−2i2−2i22i2-2-22222-2-2000000000000000000000000000000
χ6944-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000−2i22i22i2−2i222-2-2-2-222000000000000000000000000000000
χ704-44-44-4-440004-4-4404i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ714-44-44-4-440004-4-440−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ724-44-44-4-44000-444-40000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ734-44-44-4-44000-444-4000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ744-44-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000022−22−22220000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ754-44-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000−222222−2200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ764-44-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000000022−22−222200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ774-44-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000−222222−220000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ784-4-4444-4-44-4-4-4-444400000000-40000400000000000000000000000000000000000000000000000000
χ794-4-44-4-444-4-440000422−2222−22−2222−222200000022−22−22220000000000000000000000000000000000000000000000
χ804-4-44-4-444-4-4400004−2222−222222−2222−22000000−222222−220000000000000000000000000000000000000000000000

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