Finite Group Databasebeta

← Group #288072

Character table — Group #288072

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888222244888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1
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
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-11-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1111-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-11-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-1-1-1111-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-111-1-1-1111-1-1-11
χ172222222222-22-2-2-2200000000-22222-222220000-2-2-2-200000000-2-222-2-2000000000000000000000000
χ182222222222-22-2-2-2200000000-22222-2-2-2-2-20000222200000000-2-2-2-222000000000000000000000000
χ192222222222-22-2-2-2200000000-2-2-2-2-2-222220000-2-2-2-20000000022-2-222000000000000000000000000
χ202222222222-22-2-2-2200000000-2-2-2-2-2-2-2-2-2-200002222000000002222-2-2000000000000000000000000
χ2122222222-2-22-2222-222222222-20000-20000-2-2-2-20000000000000000002222000000000000-2-2000000
χ2222222222-2-22-2222-222222222-20000-20000-2-2-2-2000000000000000000-2-2-2-200000000000022000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2-2-2-20000-20000222200000000000000000022-2-2000000000000-22000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2-2-2-20000-200002222000000000000000000-2-2220000000000002-2000000
χ252222-2-2-2-22-20-200022222−2−2−2−202i2i−2i−2i02i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i2002-2000000i2i2−i2−i222−2−2000000000000
χ262222-2-2-2-22-20-200022222−2−2−2−202i2i−2i−2i0−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i200-22000000i2i2−i2−i2−2−222000000000000
χ272222-2-2-2-22-20-200022222−2−2−2−20−2i−2i2i2i02i2i−2i−2i22−2−20000i2i2i2i2−i2−i2−i2−i200-22000000−i2−i2i2i2−2−222000000000000
χ282222-2-2-2-22-20-200022222−2−2−2−20−2i−2i2i2i0−2i−2i2i2i22−2−20000−i2−i2−i2−i2i2i2i2i2002-2000000−i2−i2i2i222−2−2000000000000
χ292222-2-2-2-22-20-20002−2−2−2−2222202i2i−2i−2i02i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i2002-2000000−i2−i2i2i2−2−222000000000000
χ302222-2-2-2-22-20-20002−2−2−2−2222202i2i−2i−2i0−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i200-22000000−i2−i2i2i222−2−2000000000000
χ312222-2-2-2-22-20-20002−2−2−2−222220−2i−2i2i2i02i2i−2i−2i−2−2220000−i2−i2−i2−i2i2i2i2i200-22000000i2i2−i2−i222−2−2000000000000
χ322222-2-2-2-22-20-20002−2−2−2−222220−2i−2i2i2i0−2i−2i2i2i−2−2220000i2i2i2i2−i2−i2−i2−i2002-2000000i2i2−i2−i2−2−222000000000000
χ3322-2-2-22-2200202-2-2022-2-222-2-20000002−22−2000022−2−222−2−222−2−20000002i−2i2i−2i00000000000000i2−i2i2−i200
χ3422-2-2-22-2200202-2-2022-2-222-2-20000002−22−2000022−2−222−2−222−2−2000000−2i2i−2i2i00000000000000−i2i2−i2i200
χ3522-2-2-22-2200202-2-2022-2-222-2-2000000−22−220000−2−222−2−222−2−2220000002i−2i2i−2i00000000000000−i2i2−i2i200
χ3622-2-2-22-2200202-2-2022-2-222-2-2000000−22−220000−2−222−2−222−2−222000000−2i2i−2i2i00000000000000i2−i2i2−i200
χ3722-2-2-22-2200202-2-20-2-222-2-2220000002−22−2000022−2−2−2−222−2−2220000002i−2i−2i2i00000000000000i2−i2−i2i200
χ3822-2-2-22-2200202-2-20-2-222-2-2220000002−22−2000022−2−2−2−222−2−222000000−2i2i2i−2i00000000000000−i2i2i2−i200
χ3922-2-2-22-2200202-2-20-2-222-2-222000000−22−220000−2−22222−2−222−2−20000002i−2i−2i2i00000000000000−i2i2i2−i200
χ4022-2-2-22-2200202-2-20-2-222-2-222000000−22−220000−2−22222−2−222−2−2000000−2i2i2i−2i00000000000000i2−i2−i2i200
χ412-2-222-2-22222-2-22-2-200000000-22i−2i2i−2i20000000000002-22-22-22-22i−2i0000000000002i−2i2i−2i000000000000
χ422-2-222-2-22222-2-22-2-200000000-22i−2i2i−2i2000000000000-22-22-22-222i−2i000000000000−2i2i−2i2i000000000000
χ432-2-222-2-22222-2-22-2-200000000-2−2i2i−2i2i20000000000002-22-22-22-2−2i2i000000000000−2i2i−2i2i000000000000
χ442-2-222-2-22222-2-22-2-200000000-2−2i2i−2i2i2000000000000-22-22-22-22−2i2i0000000000002i−2i2i−2i000000000000
χ452-2-222-2-2222-2-22-22-22-22-22-22-222i−2i2i−2i-200002-22-2000000000000−2i2i000000002i−2i2i−2i0000000000000000
χ462-2-222-2-2222-2-22-22-22-22-22-22-22−2i2i−2i2i-200002-22-20000000000002i−2i00000000−2i2i−2i2i0000000000000000
χ472-2-222-2-2222-2-22-22-2-22-22-22-2222i−2i2i−2i-20000-22-22000000000000−2i2i00000000−2i2i−2i2i0000000000000000
χ482-2-222-2-2222-2-22-22-2-22-22-22-222−2i2i−2i2i-20000-22-220000000000002i−2i000000002i−2i2i−2i0000000000000000
χ492-2-222-2-22-2-2-222-2222-22-22-22-2-2000020000-22-220000000000000000000000000000002-22-200000000
χ502-2-222-2-22-2-2-222-2222-22-22-22-2-2000020000-22-22000000000000000000000000000000-22-2200000000
χ512-2-222-2-22-2-2-222-222-22-22-22-22-20000200002-22-20000000000000000000000000000002-2-2200000000
χ522-2-222-2-22-2-2-222-222-22-22-22-22-20000200002-22-2000000000000000000000000000000-222-200000000
χ532-2-22-222-22-202000-22−22−2−22−2202-2-22000002−2−222i−2i2i−2ii2−i2i2−i2−i2i2−i2i200002i−2i00002−2−22−i2i2i2−i2000000000000
χ542-2-22-222-22-202000-22−22−2−22−2202-2-22000002−2−22−2i2i−2i2i−i2i2−i2i2i2−i2i2−i20000−2i2i00002−2−22i2−i2−i2i2000000000000
χ552-2-22-222-22-202000-22−22−2−22−220-222-2000002−2−222i−2i2i−2ii2−i2i2−i2−i2i2−i2i20000−2i2i0000−222−2i2−i2−i2i2000000000000
χ562-2-22-222-22-202000-22−22−2−22−220-222-2000002−2−22−2i2i−2i2i−i2i2−i2i2i2−i2i2−i200002i−2i0000−222−2−i2i2i2−i2000000000000
χ572-2-22-222-22-202000-2−22−222−22−202-2-2200000−222−22i−2i2i−2i−i2i2−i2i2i2−i2i2−i200002i−2i0000−222−2i2−i2−i2i2000000000000
χ582-2-22-222-22-202000-2−22−222−22−202-2-2200000−222−2−2i2i−2i2ii2−i2i2−i2−i2i2−i2i20000−2i2i0000−222−2−i2i2i2−i2000000000000
χ592-2-22-222-22-202000-2−22−222−22−20-222-200000−222−22i−2i2i−2i−i2i2−i2i2i2−i2i2−i20000−2i2i00002−2−22−i2i2i2−i2000000000000
χ602-2-22-222-22-202000-2−22−222−22−20-222-200000−222−2−2i2i−2i2ii2−i2i2−i2−i2i2−i2i200002i−2i00002−2−22i2−i2−i2i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4404000-422222222−22−22−22−220000000000−22−222222000000000000000000000000000000000000000000
χ634444-4-4-4-4-4404000-4−22−22−22−222222222200000000002222−22−22000000000000000000000000000000000000000000
χ6444-4-44-44-4000000002222−22−22−22−2222220000002i2−2i2−2i22i2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6544-4-44-44-4000000002222−22−22−22−222222000000−2i22i22i2−2i200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6644-4-44-44-400000000−22−2222222222−22−220000002i2−2i2−2i22i200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6744-4-44-44-400000000−22−2222222222−22−22000000−2i22i22i2−2i2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6844-4-4-44-4400-40-44400000000000000022−2222−220000−22−22222200000000000000000000000000000000000000
χ6944-4-4-44-4400-40-444000000000000000−2222−222200002222−22−2200000000000000000000000000000000000000
χ704-44-444-4-40000000022−22−2222−222222−22000000000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ714-44-444-4-40000000022−22−2222−222222−2200000000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ724-44-444-4-400000000−222222−2222−22−2222000000000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ734-44-444-4-400000000−222222−2222−22−222200000000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ744-44-4-4-4440040-4-4400000000000000000000000000022−22−222222−22−2222000000000000000000000000000000
χ754-44-4-4-4440040-4-44000000000000000000000000000−222222−22−222222−22000000000000000000000000000000
χ764-44-4-4-44400-4044-404-4-444-4-4400000000000000000000000000000000000000000000000000000000
χ774-44-4-4-44400-4044-40-444-4-444-400000000000000000000000000000000000000000000000000000000
χ784-4-444-4-44-4-444-44-440000000040000-400000000000000000000000000000000000000000000000000
χ794-4-44-444-4-440-4000422−2222−22−2222−22220000000000−222222−22000000000000000000000000000000000000000000
χ804-4-44-444-4-440-40004−2222−222222−2222−22000000000022−22−2222000000000000000000000000000000000000000000

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