Finite Group Databasebeta

← Group #311108

Character table — Group #311108

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
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
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-11-1-11111-1-11-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1111-1-1-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-11-1-1-111-1-1111-1
χ17222222222-22-2-222-200000000-22222-200002222-2-2-2-200000000-2-2220000-2-200000000000000000000
χ18222222222-22-2-222-200000000-22222-20000-2-2-2-2222200000000-2-2-2-200002200000000000000000000
χ19222222222-22-2-222-200000000-2-2-2-2-2-200002222-2-2-2-20000000022-2-200002200000000000000000000
χ20222222222-22-2-222-200000000-2-2-2-2-2-20000-2-2-2-222220000000022220000-2-200000000000000000000
χ2122222222-22-222-2-2222222222-20000-2-2-2-2-20000000000000000000022220000000000-2-20000000000
χ2222222222-22-222-2-2222222222-20000-2-2-2-2-200000000000000000000-2-2-2-20000000000220000000000
χ2322222222-22-222-2-22-2-2-2-2-2-2-2-2-20000-222220000000000000000000022-2-200000000002-20000000000
χ2422222222-22-222-2-22-2-2-2-2-2-2-2-2-20000-2222200000000000000000000-2-2220000000000-220000000000
χ25222-2-2-2-22-20-2002202222−2−2−2−2022-2-2022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2002i−2i00000022−2−2i2i2−i2−i2000000000000
χ26222-2-2-2-22-20-2002202222−2−2−2−2022-2-2022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200−2i2i00000022−2−2−i2−i2i2i2000000000000
χ27222-2-2-2-22-20-2002202222−2−2−2−20-2-222022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200−2i2i000000−2−222−i2−i2i2i2000000000000
χ28222-2-2-2-22-20-2002202222−2−2−2−20-2-222022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2002i−2i000000−2−222i2i2−i2−i2000000000000
χ29222-2-2-2-22-20-200220−2−2−2−22222022-2-20−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2002i−2i000000−2−222−i2−i2i2i2000000000000
χ30222-2-2-2-22-20-200220−2−2−2−22222022-2-20−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200−2i2i000000−2−222i2i2−i2−i2000000000000
χ31222-2-2-2-22-20-200220−2−2−2−222220-2-2220−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200−2i2i00000022−2−2i2i2−i2−i2000000000000
χ32222-2-2-2-22-20-200220−2−2−2−222220-2-2220−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2002i−2i00000022−2−2−i2−i2i2i2000000000000
χ3322-222-2-2-20-202-20022i2i−2i−2i2i2i−2i−2i00000000002−22−222−2−2i2i2−i2−i2i2i2−i2−i200002-22i−2i0000000000000000i2−i22−200
χ3422-222-2-2-20-202-20022i2i−2i−2i2i2i−2i−2i00000000002−22−222−2−2i2i2−i2−i2i2i2−i2−i20000-22−2i2i0000000000000000−i2i2−2200
χ3522-222-2-2-20-202-20022i2i−2i−2i2i2i−2i−2i0000000000−22−22−2−222−i2−i2i2i2−i2−i2i2i200002-22i−2i0000000000000000−i2i2−2200
χ3622-222-2-2-20-202-20022i2i−2i−2i2i2i−2i−2i0000000000−22−22−2−222−i2−i2i2i2−i2−i2i2i20000-22−2i2i0000000000000000i2−i22−200
χ3722-222-2-2-20-202-2002−2i−2i2i2i−2i−2i2i2i00000000002−22−222−2−2−i2−i2i2i2−i2−i2i2i200002-2−2i2i0000000000000000−i2i22−200
χ3822-222-2-2-20-202-2002−2i−2i2i2i−2i−2i2i2i00000000002−22−222−2−2−i2−i2i2i2−i2−i2i2i20000-222i−2i0000000000000000i2−i2−2200
χ3922-222-2-2-20-202-2002−2i−2i2i2i−2i−2i2i2i0000000000−22−22−2−222i2i2−i2−i2i2i2−i2−i200002-2−2i2i0000000000000000i2−i2−2200
χ4022-222-2-2-20-202-2002−2i−2i2i2i−2i−2i2i2i0000000000−22−22−2−222i2i2−i2−i2i2i2−i2−i20000-222i−2i0000000000000000−i2i22−200
χ412-222-2-22-222-2-2-22-222i−2i2i−2i2i−2i2i−2i-2000022i−2i2i−2i0000000000000000000000000000000000002i−2i2-2000000
χ422-222-2-22-222-2-2-22-222i−2i2i−2i2i−2i2i−2i-2000022i−2i2i−2i000000000000000000000000000000000000−2i2i-22000000
χ432-222-2-22-222-2-2-22-22−2i2i−2i2i−2i2i−2i2i-200002−2i2i−2i2i0000000000000000000000000000000000002i−2i-22000000
χ442-222-2-22-222-2-2-22-22−2i2i−2i2i−2i2i−2i2i-200002−2i2i−2i2i000000000000000000000000000000000000−2i2i2-2000000
χ452-222-2-22-2-222-2-2-2222i−2i2i−2i2i−2i2i−2i22i−2i2i−2i-2−2i2i−2i2i00000000000000002i−2i000000002-22-20000000000000000
χ462-222-2-22-2-222-2-2-2222i−2i2i−2i2i−2i2i−2i2−2i2i−2i2i-2−2i2i−2i2i0000000000000000−2i2i00000000-22-220000000000000000
χ472-222-2-22-2-222-2-2-222−2i2i−2i2i−2i2i−2i2i22i−2i2i−2i-22i−2i2i−2i00000000000000002i−2i00000000-22-220000000000000000
χ482-222-2-22-2-222-2-2-222−2i2i−2i2i−2i2i−2i2i2−2i2i−2i2i-22i−2i2i−2i0000000000000000−2i2i000000002-22-20000000000000000
χ492-222-2-22-2-2-2222-22-200000000-22i−2i2i−2i20000000000002-22-22-22-2−2i2i0000000000002i−2i2i−2i000000000000
χ502-222-2-22-2-2-2222-22-200000000-22i−2i2i−2i2000000000000-22-22-22-22−2i2i000000000000−2i2i−2i2i000000000000
χ512-222-2-22-2-2-2222-22-200000000-2−2i2i−2i2i20000000000002-22-22-22-22i−2i000000000000−2i2i−2i2i000000000000
χ522-222-2-22-2-2-2222-22-200000000-2−2i2i−2i2i2000000000000-22-22-22-222i−2i0000000000002i−2i2i−2i000000000000
χ532-22-222-2-220-200-220i2−i2i2−i2−i2i2−i2i202i−2i−2i2i0−i2i2i2−i200002-22-2i2−i2i2−i2−i2i2−i2i2000000002i−2i2−2−22−222−2000000000000
χ542-22-222-2-220-200-220i2−i2i2−i2−i2i2−i2i202i−2i−2i2i0−i2i2i2−i20000-22-22−i2i2−i2i2i2−i2i2−i200000000−2i2i2−2−222−2−22000000000000
χ552-22-222-2-220-200-220i2−i2i2−i2−i2i2−i2i20−2i2i2i−2i0−i2i2i2−i200002-22-2i2−i2i2−i2−i2i2−i2i200000000−2i2i−222−22−2−22000000000000
χ562-22-222-2-220-200-220i2−i2i2−i2−i2i2−i2i20−2i2i2i−2i0−i2i2i2−i20000-22-22−i2i2−i2i2i2−i2i2−i2000000002i−2i−222−2−222−2000000000000
χ572-22-222-2-220-200-220−i2i2−i2i2i2−i2i2−i202i−2i−2i2i0i2−i2−i2i200002-22-2−i2i2−i2i2i2−i2i2−i2000000002i−2i−222−22−2−22000000000000
χ582-22-222-2-220-200-220−i2i2−i2i2i2−i2i2−i202i−2i−2i2i0i2−i2−i2i20000-22-22i2−i2i2−i2−i2i2−i2i200000000−2i2i−222−2−222−2000000000000
χ592-22-222-2-220-200-220−i2i2−i2i2i2−i2i2−i20−2i2i2i−2i0i2−i2−i2i200002-22-2−i2i2−i2i2i2−i2i2−i200000000−2i2i2−2−22−222−2000000000000
χ602-22-222-2-220-200-220−i2i2−i2i2i2−i2i2−i20−2i2i2i−2i0i2−i2−i2i20000-22-22i2−i2i2−i2−i2i2−i2i2000000002i−2i2−2−222−2−22000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-4-4440400-4-4022222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ63444-4-4-4-4440400-4-40−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-444-4-4-4040-4400-400000000000000000022−2222−22−22−22222200000000000000000000000000000000000000
χ6544-444-4-4-4040-4400-4000000000000000000−2222−22222222−22−2200000000000000000000000000000000000000
χ6644-4-4-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000002i2−2i2−2i22i20000-2-22222-2-2000000000000000000000000000000
χ6744-4-4-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000022-2-2-2-222000000000000000000000000000000
χ6844-4-4-444-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000022-2-2-2-222000000000000000000000000000000
χ6944-4-4-444-400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000−2i22i22i2−2i20000-2-22222-2-2000000000000000000000000000000
χ704-444-4-44-44-4-4444-4-40000000040000-400000000000000000000000000000000000000000000000000
χ714-44-444-4-4-404004-402i2−2i22i2−2i2−2i22i2−2i22i20000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ724-44-444-4-4-404004-40−2i22i2−2i22i22i2−2i22i2−2i2000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ734-4-44-44-440404-400-4000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ744-4-44-44-440404-400-400000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ754-4-44-44-440-40-440044-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ764-4-44-44-440-40-44004-444-4-444-400000000000000000000000000000000000000000000000000000000
χ774-4-4-44-4440000000022−22−2222−222222−220000000000000022−22−22222-2-22-222-2000000000000000000000000000000
χ784-4-4-44-4440000000022−22−2222−222222−2200000000000000−222222−22-222-22-2-22000000000000000000000000000000
χ794-4-4-44-44400000000−222222−2222−22−22220000000000000022−22−2222-222-22-2-22000000000000000000000000000000
χ804-4-4-44-44400000000−222222−2222−22−222200000000000000−222222−222-2-22-222-2000000000000000000000000000000

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