Finite Group Databasebeta

← Group #229359

Character table — Group #229359

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222244444444444444444444444444888888888888888888888888888816161616161616161616
order12222222444444444444444444444488888888888844444444448888888888888888882244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ511111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-11111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-111
χ1711-11-1-11-1-111-1-1-111ii−i−iii−i−iii−i−i1-111-1-1iiii−i−i−i−ii−i1-11-1i−ii−iii−i−i1-111-1-111-1-1ii−i−i1-1i−i1-1i−i1-1
χ1811-11-1-11-1-111-1-1-111ii−i−iii−i−iii−i−i1-111-1-1−i−i−i−iiiiii−i-11-11i−ii−iii−i−i1-1-1-111-1-111−i−iii1-1−ii1-1−ii-11
χ1911-11-1-11-1-111-1-1-111ii−i−iii−i−i−i−iii1-1-1-111iiii−i−i−i−ii−i1-11-1i−i−ii−i−iii-1111-1-1-1-111−i−iii1-1i−i-11−ii-11
χ2011-11-1-11-1-111-1-1-111ii−i−iii−i−i−i−iii1-1-1-111−i−i−i−iiiiii−i-11-11i−i−ii−i−iii-11-1-11111-1-1ii−i−i1-1−ii-11i−i1-1
χ2111-11-1-11-1-111-1-1-111ii−i−i−i−iiiii−i−i1-111-1-1iiii−i−i−i−ii−i-11-11−iii−i−i−iii1-111-1-111-1-1ii−i−i-11−ii-11−ii-11
χ2211-11-1-11-1-111-1-1-111ii−i−i−i−iiiii−i−i1-111-1-1−i−i−i−iiiiii−i1-11-1−iii−i−i−iii1-1-1-111-1-111−i−iii-11i−i-11i−i1-1
χ2311-11-1-11-1-111-1-1-111ii−i−i−i−iii−i−iii1-1-1-111iiii−i−i−i−ii−i-11-11−ii−iiii−i−i-1111-1-1-1-111−i−iii-11−ii1-1i−i1-1
χ2411-11-1-11-1-111-1-1-111ii−i−i−i−iii−i−iii1-1-1-111−i−i−i−iiiiii−i1-11-1−ii−iiii−i−i-11-1-11111-1-1ii−i−i-11i−i1-1−ii-11
χ2511-11-1-11-1-111-1-1-111−i−iiiii−i−iii−i−i1-1-1-111iiii−i−i−i−i−ii1-11-1i−ii−i−i−iii-11-1-11111-1-1−i−iii-11−ii1-1i−i-11
χ2611-11-1-11-1-111-1-1-111−i−iiiii−i−iii−i−i1-1-1-111−i−i−i−iiiii−ii-11-11i−ii−i−i−iii-1111-1-1-1-111ii−i−i-11i−i1-1−ii1-1
χ2711-11-1-11-1-111-1-1-111−i−iiiii−i−i−i−iii1-111-1-1iiii−i−i−i−i−ii1-11-1i−i−iiii−i−i1-1-1-111-1-111ii−i−i-11−ii-11−ii1-1
χ2811-11-1-11-1-111-1-1-111−i−iiiii−i−i−i−iii1-111-1-1−i−i−i−iiiii−ii-11-11i−i−iiii−i−i1-111-1-111-1-1−i−iii-11i−i-11i−i-11
χ2911-11-1-11-1-111-1-1-111−i−iii−i−iiiii−i−i1-1-1-111iiii−i−i−i−i−ii-11-11−iii−iii−i−i-11-1-11111-1-1−i−iii1-1i−i-11−ii1-1
χ3011-11-1-11-1-111-1-1-111−i−iii−i−iiiii−i−i1-1-1-111−i−i−i−iiiii−ii1-11-1−iii−iii−i−i-1111-1-1-1-111ii−i−i1-1−ii-11i−i-11
χ3111-11-1-11-1-111-1-1-111−i−iii−i−iii−i−iii1-111-1-1iiii−i−i−i−i−ii-11-11−ii−ii−i−iii1-1-1-111-1-111ii−i−i1-1i−i1-1i−i-11
χ3211-11-1-11-1-111-1-1-111−i−iii−i−iii−i−iii1-111-1-1−i−i−i−iiiii−ii1-11-1−ii−ii−i−iii1-111-1-111-1-1−i−iii1-1−ii1-1−ii1-1
χ33222222222-22-2-222-2222200002222-2-2222200000000-2-2000000-2-20000-2-20000000000000000000000
χ34222222222-22-2-222-222220000-2-2-2-2-2-2-2-2-2-200000000-2-2000000220000220000000000000000000000
χ35222222222-22-2-222-2-2-2-2-200002222-2-2-2-2-2-20000000022000000-2-20000220000000000000000000000
χ36222222222-22-2-222-2-2-2-2-20000-2-2-2-2-2-222220000000022000000220000-2-20000000000000000000000
χ3722222222-22-222-2-22000022220000-2-2000022-2-222-2-20022-2-2-2-2000000000000000000000000000000
χ3822222222-22-222-2-22000022220000-2-20000-2-222-2-22200-2-222-2-2000000000000000000000000000000
χ3922222222-22-222-2-220000-2-2-2-20000-2-2000022-2-222-2-200-2-22222000000000000000000000000000000
χ4022222222-22-222-2-220000-2-2-2-20000-2-20000-2-222-2-2220022-2-222000000000000000000000000000000
χ41222-2-22-2-2-20-2002202i−2i2i−2i00002-22-2002i−2i2i−2i2−22−22−22−20000000000000000i2−i2i2−i22−22−2i2−i2i2−i20000000000
χ42222-2-22-2-2-20-2002202i−2i2i−2i00002-22-2002i−2i2i−2i−22−22−22−220000000000000000−i2i2−i2i2−22−22−i2i2−i2i20000000000
χ43222-2-22-2-2-20-2002202i−2i2i−2i0000-22-2200−2i2i−2i2i2−22−22−22−20000000000000000i2−i2i2−i2−22−22−i2i2−i2i20000000000
χ44222-2-22-2-2-20-2002202i−2i2i−2i0000-22-2200−2i2i−2i2i−22−22−22−220000000000000000−i2i2−i2i22−22−2i2−i2i2−i20000000000
χ45222-2-22-2-2-20-200220−2i2i−2i2i00002-22-200−2i2i−2i2i2−22−22−22−20000000000000000−i2i2−i2i22−22−2−i2i2−i2i20000000000
χ46222-2-22-2-2-20-200220−2i2i−2i2i00002-22-200−2i2i−2i2i−22−22−22−220000000000000000i2−i2i2−i2−22−22i2−i2i2−i20000000000
χ47222-2-22-2-2-20-200220−2i2i−2i2i0000-22-22002i−2i2i−2i2−22−22−22−20000000000000000−i2i2−i2i2−22−22i2−i2i2−i20000000000
χ48222-2-22-2-2-20-200220−2i2i−2i2i0000-22-22002i−2i2i−2i−22−22−22−220000000000000000i2−i2i2−i22−22−2−i2i2−i2i20000000000
χ4922-22-2-22-222-2-2-22-2200002i2i−2i−2i0000-2200002i2i−2i−2i−2i−2i2i2i002-2-22−2i2i000000000000000000000000000000
χ5022-22-2-22-222-2-2-22-2200002i2i−2i−2i0000-220000−2i−2i2i2i2i2i−2i−2i00-222-2−2i2i000000000000000000000000000000
χ5122-22-2-22-222-2-2-22-220000−2i−2i2i2i0000-2200002i2i−2i−2i−2i−2i2i2i00-222-22i−2i000000000000000000000000000000
χ5222-22-2-22-222-2-2-22-220000−2i−2i2i2i0000-220000−2i−2i2i2i2i2i−2i−2i002-2-222i−2i000000000000000000000000000000
χ5322-22-2-22-2-2-2222-22-22i2i−2i−2i00002i2i−2i−2i-2222-2-200000000−2i2i000000−2i2i0000-220000000000000000000000
χ5422-22-2-22-2-2-2222-22-22i2i−2i−2i0000−2i−2i2i2i-22-2-22200000000−2i2i0000002i−2i00002-20000000000000000000000
χ5522-22-2-22-2-2-2222-22-2−2i−2i2i2i00002i2i−2i−2i-22-2-222000000002i−2i000000−2i2i00002-20000000000000000000000
χ5622-22-2-22-2-2-2222-22-2−2i−2i2i2i0000−2i−2i2i2i-2222-2-2000000002i−2i0000002i−2i0000-220000000000000000000000
χ5722-2-22-2-2220-200-2202-2-2200002i−2i−2i2i00−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i22−2−222−2−220000000000
χ5822-2-22-2-2220-200-2202-2-2200002i−2i−2i2i00−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i2−222−2−222−20000000000
χ5922-2-22-2-2220-200-2202-2-220000−2i2i2i−2i002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000−i2i2i2−i2−222−2−222−20000000000
χ6022-2-22-2-2220-200-2202-2-220000−2i2i2i−2i002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000i2−i2−i2i22−2−222−2−220000000000
χ6122-2-22-2-2220-200-220-222-200002i−2i−2i2i002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i22−2−22−222−20000000000
χ6222-2-22-2-2220-200-220-222-200002i−2i−2i2i002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i2−222−22−2−220000000000
χ6322-2-22-2-2220-200-220-222-20000−2i2i2i−2i00−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000000000i2−i2−i2i2−222−22−2−220000000000
χ6422-2-22-2-2220-200-220-222-20000−2i2i2i−2i00−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20000000000000000−i2i2i2−i22−2−22−222−20000000000
χ6544444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ66444-4-44-4-440400-4-4000000000000000000022−22−222222−22−222200000000000000000000000000000000000000
χ67444-4-44-4-440400-4-40000000000000000000−222222−22−222222−2200000000000000000000000000000000000000
χ6844-44-4-44-44-4-4444-4-40000000000004-400000000000000000000000000000000000000000000000000
χ6944-4-44-4-44-404004-400000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ7044-4-44-4-44-404004-40000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ714-4444-4-4-40404-400-400004-44-400000000000000000000000000000000000000000000000000000000
χ724-4444-4-4-40404-400-40000-44-4400000000000000000000000000000000000000000000000000000000
χ734-4444-4-4-40-40-440040000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ744-4444-4-4-40-40-44004000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ754-4-44-44-44040-4400-400004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ764-4-44-44-44040-4400-40000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ774-4-44-44-440-404-400400000000000000000000000000000000000022−22−2222000000000000000000000000
χ784-4-44-44-440-404-4004000000000000000000000000000000000000−222222−22000000000000000000000000
χ798-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000

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