Finite Group Databasebeta

← Group #288097

Character table — Group #288097

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111111-1-1-111-1-1-11
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-11-1-111-1-11-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11-111-1-111-11
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-111-11-1-1-1-111-11
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-1-11-11111-1-11-1
χ17222222222-2-22-222-222222222-20000-20000-2-2-2-200000000000000002222000000000000-2-200000000
χ18222222222-2-22-222-222222222-20000-20000-2-2-2-20000000000000000-2-2-2-20000000000002200000000
χ19222222222-2-22-222-2-2-2-2-2-2-2-2-2-20000-200002222000000000000000022-2-20000000000002-200000000
χ20222222222-2-22-222-2-2-2-2-2-2-2-2-2-20000-2000022220000000000000000-2-222000000000000-2200000000
χ2122222222-222-22-2-2200000000-22222-222220000-2-2-2-200000000-2-2220000-2-200000000000000000000
χ2222222222-222-22-2-2200000000-22222-2-2-2-2-20000222200000000-2-2-2-200002200000000000000000000
χ2322222222-222-22-2-2200000000-2-2-2-2-2-222220000-2-2-2-20000000022-2-200002200000000000000000000
χ2422222222-222-22-2-2200000000-2-2-2-2-2-2-2-2-2-2000022220000000022220000-2-200000000000000000000
χ25222-2-22-2-2-200-202202i2i2i2i−2i−2i−2i−2i00000022−2−2000022−2−2i2i2i2i2−i2−i2−i2−i200002-22i−2i00000000000000002−2i2−i200
χ26222-2-22-2-2-200-202202i2i2i2i−2i−2i−2i−2i00000022−2−2000022−2−2i2i2i2i2−i2−i2−i2−i20000-22−2i2i0000000000000000−22−i2i200
χ27222-2-22-2-2-200-202202i2i2i2i−2i−2i−2i−2i000000−2−2220000−2−222−i2−i2−i2−i2i2i2i2i200002-22i−2i0000000000000000−22−i2i200
χ28222-2-22-2-2-200-202202i2i2i2i−2i−2i−2i−2i000000−2−2220000−2−222−i2−i2−i2−i2i2i2i2i20000-22−2i2i00000000000000002−2i2−i200
χ29222-2-22-2-2-200-20220−2i−2i−2i−2i2i2i2i2i00000022−2−2000022−2−2−i2−i2−i2−i2i2i2i2i200002-2−2i2i00000000000000002−2−i2i200
χ30222-2-22-2-2-200-20220−2i−2i−2i−2i2i2i2i2i00000022−2−2000022−2−2−i2−i2−i2−i2i2i2i2i20000-222i−2i0000000000000000−22i2−i200
χ31222-2-22-2-2-200-20220−2i−2i−2i−2i2i2i2i2i000000−2−2220000−2−222i2i2i2i2−i2−i2−i2−i200002-2−2i2i0000000000000000−22i2−i200
χ32222-2-22-2-2-200-20220−2i−2i−2i−2i2i2i2i2i000000−2−2220000−2−222i2i2i2i2−i2−i2−i2−i20000-222i−2i00000000000000002−2−i2i200
χ3322-22-2-2-2202-20200-222−2−222−2−202i2i−2i−2i02-22-222−2−2000022−2−222−2−2002i−2i000000i2i2−i2−i2i2i2−i2−i2000000000000
χ3422-22-2-2-2202-20200-222−2−222−2−202i2i−2i−2i0-22-2222−2−20000−2−222−2−22200−2i2i000000i2i2−i2−i2−i2−i2i2i2000000000000
χ3522-22-2-2-2202-20200-222−2−222−2−20−2i−2i2i2i02-22-222−2−2000022−2−222−2−200−2i2i000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3622-22-2-2-2202-20200-222−2−222−2−20−2i−2i2i2i0-22-2222−2−20000−2−222−2−222002i−2i000000−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-22-2-2-2202-20200-2−2−222−2−22202i2i−2i−2i02-22-2−2−2220000−2−222−2−222002i−2i000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3822-22-2-2-2202-20200-2−2−222−2−22202i2i−2i−2i0-22-22−2−222000022−2−222−2−200−2i2i000000−i2−i2i2i2i2i2−i2−i2000000000000
χ3922-22-2-2-2202-20200-2−2−222−2−2220−2i−2i2i2i02-22-2−2−2220000−2−222−2−22200−2i2i000000i2i2−i2−i2i2i2−i2−i2000000000000
χ4022-22-2-2-2202-20200-2−2−222−2−2220−2i−2i2i2i0-22-22−2−222000022−2−222−2−2002i−2i000000i2i2−i2−i2−i2−i2i2i2000000000000
χ412-22-22-2-22222-2-22-2-200000000-22i−2i2i−2i20000000000002-22-22-22-22i−2i0000000000002i−2i2i−2i000000000000
χ422-22-22-2-22222-2-22-2-200000000-22i−2i2i−2i2000000000000-22-22-22-222i−2i000000000000−2i2i−2i2i000000000000
χ432-22-22-2-22222-2-22-2-200000000-2−2i2i−2i2i20000000000002-22-22-22-2−2i2i000000000000−2i2i−2i2i000000000000
χ442-22-22-2-22222-2-22-2-200000000-2−2i2i−2i2i2000000000000-22-22-22-22−2i2i0000000000002i−2i2i−2i000000000000
χ452-22-22-2-22-2222-2-22-22-22-22-22-222i−2i2i−2i-200002-22-2000000000000−2i2i000000002i−2i2i−2i0000000000000000
χ462-22-22-2-22-2222-2-22-22-22-22-22-22−2i2i−2i2i-200002-22-20000000000002i−2i00000000−2i2i−2i2i0000000000000000
χ472-22-22-2-22-2222-2-22-2-22-22-22-2222i−2i2i−2i-20000-22-22000000000000−2i2i00000000−2i2i−2i2i0000000000000000
χ482-22-22-2-22-2222-2-22-2-22-22-22-222−2i2i−2i2i-20000-22-220000000000002i−2i000000002i−2i2i−2i0000000000000000
χ492-22-22-2-22-2-2-222-2222-22-22-22-2-2000020000-22-220000000000000000000000000000002-2002-2000000
χ502-22-22-2-22-2-2-222-2222-22-22-22-2-2000020000-22-22000000000000000000000000000000-2200-22000000
χ512-22-22-2-22-2-2-222-222-22-22-22-22-20000200002-22-20000000000000000000000000000002-200-22000000
χ522-22-22-2-22-2-2-222-222-22-22-22-22-20000200002-22-2000000000000000000000000000000-22002-2000000
χ532-2-2-2-222202-20-20022−2−222−2−2202-2-22000002−2−222-22-22−2−222−2−22000000002-22−2−222−2−22000000000000
χ542-2-2-2-222202-20-20022−2−222−2−2202-2-22000002−2−22-22-22−222−2−222−200000000-222−2−22−222−2000000000000
χ552-2-2-2-222202-20-20022−2−222−2−220-222-2000002−2−222-22-22−2−222−2−2200000000-22−222−2−222−2000000000000
χ562-2-2-2-222202-20-20022−2−222−2−220-222-2000002−2−22-22-22−222−2−222−2000000002-2−222−22−2−22000000000000
χ572-2-2-2-222202-20-2002−222−2−222−202-2-2200000−222−22-22-2−222−2−222−2000000002-2−222−2−222−2000000000000
χ582-2-2-2-222202-20-2002−222−2−222−202-2-2200000−222−2-22-222−2−222−2−2200000000-22−222−22−2−22000000000000
χ592-2-2-2-222202-20-2002−222−2−222−20-222-200000−222−22-22-2−222−2−222−200000000-222−2−222−2−22000000000000
χ602-2-2-2-222202-20-2002−222−2−222−20-222-200000−222−2-22-222−2−222−2−22000000002-22−2−22−222−2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-44-4-440040-4-40000000000000002222−22−220000−22−22222200000000000000000000000000000000000000
χ63444-4-44-4-440040-4-4000000000000000−22−22222200002222−22−2200000000000000000000000000000000000000
χ6444-44-4-4-440-440-40042222−22−222222−22−220000000000−22−222222000000000000000000000000000000000000000000
χ6544-44-4-4-440-440-4004−22−222222−22−22222200000000002222−22−22000000000000000000000000000000000000000000
χ6644-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000022−22−2222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6744-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i2000000−222222−2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6844-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i200000022−22−222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6944-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000−222222−22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ704-444-4-44-4400-40-4404i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ714-444-4-44-4400-40-440−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ724-444-4-44-4-400404-40000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ734-444-4-44-4-400404-4000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ744-44-44-4-444-4-4-444-440000000040000-400000000000000000000000000000000000000000000000000
χ754-4-4444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000022−22−22222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ764-4-4444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000−222222−22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ774-4-4444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000022−22−2222−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ784-4-4444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000−222222−222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ794-4-4-4-44440-440400-422−22−222222−22−22220000000000−222222−22000000000000000000000000000000000000000000
χ804-4-4-4-44440-440400-4−222222−22−222222−22000000000022−22−2222000000000000000000000000000000000000000000

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