Finite Group Databasebeta

← Group #308921

Character table — Group #308921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
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
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ172222222222-2-22-2-2200000000-22222-200002222-2-2-2-200000000-2-222-2-2000000000000000000000000
χ182222222222-2-22-2-2200000000-22222-20000-2-2-2-2222200000000-2-2-2-222000000000000000000000000
χ192222222222-2-22-2-2200000000-2-2-2-2-2-200002222-2-2-2-20000000022-2-222000000000000000000000000
χ202222222222-2-22-2-2200000000-2-2-2-2-2-20000-2-2-2-22222000000002222-2-2000000000000000000000000
χ2122222222-2-222-222-222222222-20000-2-2-2-2-20000000000000000000000222200000000-2-20000000000
χ2222222222-2-222-222-222222222-20000-2-2-2-2-20000000000000000000000-2-2-2-200000000220000000000
χ2322222222-2-222-222-2-2-2-2-2-2-2-2-2-20000-22222000000000000000000000022-2-200000000-220000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-2-20000-222220000000000000000000000-2-222000000002-20000000000
χ25222-2-2-22-22222-2-2-2-22222-2-2-2-220000-222-2-20000000000000000000000000000000000002-22-2000000
χ26222-2-2-22-22222-2-2-2-22222-2-2-2-220000-222-2-2000000000000000000000000000000000000-22-22000000
χ27222-2-2-22-22222-2-2-2-2-2-2-2-2222220000-2-2-2220000000000000000000000000000000000002-2-22000000
χ28222-2-2-22-22222-2-2-2-2-2-2-2-2222220000-2-2-222000000000000000000000000000000000000-222-2000000
χ29222-2-2-22-2-2-2222-2-222222-2-2-2-2-22i2i−2i−2i2-2-22200000000000000002i−2i000000002i2i−2i−2i0000000000000000
χ30222-2-2-22-2-2-2222-2-222222-2-2-2-2-2−2i−2i2i2i2-2-2220000000000000000−2i2i00000000−2i−2i2i2i0000000000000000
χ31222-2-2-22-2-2-2222-2-22-2-2-2-22222-22i2i−2i−2i222-2-200000000000000002i−2i00000000−2i−2i2i2i0000000000000000
χ32222-2-2-22-2-2-2222-2-22-2-2-2-22222-2−2i−2i2i2i222-2-20000000000000000−2i2i000000002i2i−2i−2i0000000000000000
χ33222-2-2-22-2-2-2-2-222220000000022i2i−2i−2i-20000000000002i2i2i2i−2i−2i−2i−2i−2i2i00000000000022-2-2000000000000
χ34222-2-2-22-2-2-2-2-222220000000022i2i−2i−2i-2000000000000−2i−2i−2i−2i2i2i2i2i−2i2i000000000000-2-222000000000000
χ35222-2-2-22-2-2-2-2-22222000000002−2i−2i2i2i-20000000000002i2i2i2i−2i−2i−2i−2i2i−2i000000000000-2-222000000000000
χ36222-2-2-22-2-2-2-2-22222000000002−2i−2i2i2i-2000000000000−2i−2i−2i−2i2i2i2i2i2i−2i00000000000022-2-2000000000000
χ3722-22-2-2-22002-202-2022-2-222-2-20000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000002-22-200000000000000i2−i2i2−i200
χ3822-22-2-2-22002-202-2022-2-222-2-20000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000-22-2200000000000000−i2i2−i2i200
χ3922-22-2-2-22002-202-2022-2-222-2-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000002-22-200000000000000−i2i2−i2i200
χ4022-22-2-2-22002-202-2022-2-222-2-20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000-22-2200000000000000i2−i2i2−i200
χ4122-22-2-2-22002-202-20-2-222-2-2220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000002-2-2200000000000000i2−i2−i2i200
χ4222-22-2-2-22002-202-20-2-222-2-2220000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000-222-200000000000000−i2i2i2−i200
χ4322-22-2-2-22002-202-20-2-222-2-2220000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000002-2-2200000000000000−i2i2i2−i200
χ4422-22-2-2-22002-202-20-2-222-2-2220000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000-222-200000000000000i2−i2−i2i200
χ452-2-222-22-22-200-20022−22−22−22−202i−2i2i−2i02−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i2002-2000000i2−i2i2−i22−22−2000000000000
χ462-2-222-22-22-200-20022−22−22−22−202i−2i2i−2i02−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i200-22000000i2−i2i2−i2−22−22000000000000
χ472-2-222-22-22-200-20022−22−22−22−20−2i2i−2i2i02−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i200-22000000−i2i2−i2i2−22−22000000000000
χ482-2-222-22-22-200-20022−22−22−22−20−2i2i−2i2i02−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i2002-2000000−i2i2−i2i22−22−2000000000000
χ492-2-222-22-22-200-2002−22−22−22−2202i−2i2i−2i0−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i2002-2000000−i2i2−i2i2−22−22000000000000
χ502-2-222-22-22-200-2002−22−22−22−2202i−2i2i−2i0−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i200-22000000−i2i2−i2i22−22−2000000000000
χ512-2-222-22-22-200-2002−22−22−22−220−2i2i−2i2i0−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i200-22000000i2−i2i2−i22−22−2000000000000
χ522-2-222-22-22-200-2002−22−22−22−220−2i2i−2i2i0−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i2002-2000000i2−i2i2−i2−22−22000000000000
χ532-2-2-2-2222-2200-20022−22−2−22−2202-2-220−222−200002-22-22−22−2−22−2200002-200002−2−222−2−22000000000000
χ542-2-2-2-2222-2200-20022−22−2−22−2202-2-220−222−20000-22-22−22−222−22−20000-2200002−2−22−222−2000000000000
χ552-2-2-2-2222-2200-20022−22−2−22−220-222-20−222−200002-22-22−22−2−22−220000-220000−222−2−222−2000000000000
χ562-2-2-2-2222-2200-20022−22−2−22−220-222-20−222−20000-22-22−22−222−22−200002-20000−222−22−2−22000000000000
χ572-2-2-2-2222-2200-2002−22−222−22−202-2-2202−2−2200002-22-2−22−222−22−200002-20000−222−2−222−2000000000000
χ582-2-2-2-2222-2200-2002−22−222−22−202-2-2202−2−220000-22-222−22−2−22−220000-220000−222−22−2−22000000000000
χ592-2-2-2-2222-2200-2002−22−222−22−20-222-202−2−2200002-22-2−22−222−22−20000-2200002−2−222−2−22000000000000
χ602-2-2-2-2222-2200-2002−22−222−22−20-222-202−2−220000-22-222−22−2−22−2200002-200002−2−22−222−2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-44-444-4-4-444-400000000-40000400000000000000000000000000000000000000000000000000
χ6344-44-4-4-4400-440-4400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ6444-44-4-4-4400-440-440000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6544-4-444-4-4004-40-44044-4-4-4-44400000000000000000000000000000000000000000000000000000000
χ6644-4-444-4-4004-40-440-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ6744-4-444-4-400-4404-40000000000000000000000000002222−22−22−22−222222000000000000000000000000000000
χ6844-4-444-4-400-4404-4000000000000000000000000000−22−2222222222−22−22000000000000000000000000000000
χ694-444-44-4-40000000022−22−222222−22−2222000000000022−22−222200002-2-222-2-22000000000000000000000000000000
χ704-444-44-4-40000000022−22−222222−22−22220000000000−222222−220000-222-2-222-2000000000000000000000000000000
χ714-444-44-4-400000000−222222−22−222222−22000000000022−22−22220000-222-2-222-2000000000000000000000000000000
χ724-444-44-4-400000000−222222−22−222222−220000000000−222222−2200002-2-222-2-22000000000000000000000000000000
χ734-44-44-4-440000000022−22−2222−222222−22000000000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ744-44-44-4-440000000022−22−2222−222222−2200000000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ754-44-44-4-4400000000−222222−2222−22−2222000000000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ764-44-44-4-4400000000−222222−2222−22−222200000000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ774-4-444-44-4-4400400-422−2222−2222−2222−22000000−2222−22220000000000000000000000000000000000000000000000
χ784-4-444-44-4-4400400-4−2222−2222−2222−222200000022−2222−220000000000000000000000000000000000000000000000
χ794-4-4-4-44444-400400-422−2222−22−2222−222200000022−22−22220000000000000000000000000000000000000000000000
χ804-4-4-4-44444-400400-4−2222−222222−2222−22000000−222222−220000000000000000000000000000000000000000000000

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