Finite Group Databasebeta

← Group #229391

Character table — Group #229391

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12222222444444448888888844444444448888888888888888888844444444444488888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-11111-1-1
χ1711-11-1-11-1-11-1-1-1111iiii−i−i−i−i1ii−i−iii−i−i-1ii−i−i11-1-111-1-1iiii−i−i−i−ii−i1-1i−i1-1i−ii−i11-1-111-1-11-1i−i1-1i−ii−i1-1
χ1811-11-1-11-1-11-1-1-1111iiii−i−i−i−i1ii−i−iii−i−i-1ii−i−i11-1-111-1-1iiii−i−i−i−ii−i-11−ii-11i−i−ii11-1-111-1-1-11−ii-11−ii−ii-11
χ1911-11-1-11-1-11-1-1-1111iiii−i−i−i−i1ii−i−i−i−iii-1ii−i−i-1-111-1-111−i−i−i−iiiiii−i1-1i−i1-1−iii−i11-1-1-1-1111-1i−i-11−ii−ii-11
χ2011-11-1-11-1-11-1-1-1111iiii−i−i−i−i1ii−i−i−i−iii-1ii−i−i-1-111-1-111−i−i−i−iiiiii−i-11−ii-11−ii−ii11-1-1-1-111-11−ii1-1i−ii−i1-1
χ2111-11-1-11-1-11-1-1-1111iiii−i−i−i−i1−i−iiiii−i−i-1ii−i−i-1-111-1-111−i−i−i−iiiii−ii1-1i−i1-1i−ii−i-1-11111-1-1-11−ii1-1i−i−ii-11
χ2211-11-1-11-1-11-1-1-1111iiii−i−i−i−i1−i−iiiii−i−i-1ii−i−i-1-111-1-111−i−i−i−iiiii−ii-11−ii-11i−i−ii-1-11111-1-11-1i−i-11−iii−i1-1
χ2311-11-1-11-1-11-1-1-1111iiii−i−i−i−i1−i−iii−i−iii-1ii−i−i11-1-111-1-1iiii−i−i−i−i−ii1-1i−i1-1−iii−i-1-111-1-111-11−ii-11−iii−i1-1
χ2411-11-1-11-1-11-1-1-1111iiii−i−i−i−i1−i−iii−i−iii-1ii−i−i11-1-111-1-1iiii−i−i−i−i−ii-11−ii-11−ii−ii-1-111-1-1111-1i−i1-1i−i−ii-11
χ2511-11-1-11-1-11-1-1-1111−i−i−i−iiiii1ii−i−iii−i−i-1−i−iii11-1-111-1-1−i−i−i−iiiiii−i1-1−ii1-1i−i−ii-1-111-1-111-11i−i-11i−i−ii1-1
χ2611-11-1-11-1-11-1-1-1111−i−i−i−iiiii1ii−i−iii−i−i-1−i−iii11-1-111-1-1−i−i−i−iiiiii−i-11i−i-11i−ii−i-1-111-1-1111-1−ii1-1−iii−i-11
χ2711-11-1-11-1-11-1-1-1111−i−i−i−iiiii1ii−i−i−i−iii-1−i−iii-1-111-1-111iiii−i−i−i−ii−i1-1−ii1-1−ii−ii-1-11111-1-1-11i−i1-1−iii−i-11
χ2811-11-1-11-1-11-1-1-1111−i−i−i−iiiii1ii−i−i−i−iii-1−i−iii-1-111-1-111iiii−i−i−i−ii−i-11i−i-11−iii−i-1-11111-1-11-1−ii-11i−i−ii1-1
χ2911-11-1-11-1-11-1-1-1111−i−i−i−iiiii1−i−iiiii−i−i-1−i−iii-1-111-1-111iiii−i−i−i−i−ii1-1−ii1-1i−i−ii11-1-1-1-1111-1−ii-11i−ii−i-11
χ3011-11-1-11-1-11-1-1-1111−i−i−i−iiiii1−i−iiiii−i−i-1−i−iii-1-111-1-111iiii−i−i−i−i−ii-11i−i-11i−ii−i11-1-1-1-111-11i−i1-1−ii−ii1-1
χ3111-11-1-11-1-11-1-1-1111−i−i−i−iiiii1−i−iii−i−iii-1−i−iii11-1-111-1-1−i−i−i−iiiii−ii1-1−ii1-1−ii−ii11-1-111-1-11-1−ii1-1−ii−ii1-1
χ3211-11-1-11-1-11-1-1-1111−i−i−i−iiiii1−i−iii−i−iii-1−i−iii11-1-111-1-1−i−i−i−iiiii−ii-11i−i-11−iii−i11-1-111-1-1-11i−i-11i−ii−i-11
χ332222222222-2-22-2-2200000000-222222222-200002222-2-2-2-200000000-2-2000000-2-20000000000000000000000
χ342222222222-2-22-2-2200000000-22222-2-2-2-2-20000-2-2-2-2222200000000-2-2000000220000000000000000000000
χ352222222222-2-22-2-2200000000-2-2-2-2-22222-20000-2-2-2-222220000000022000000-2-20000000000000000000000
χ362222222222-2-22-2-2200000000-2-2-2-2-2-2-2-2-2-200002222-2-2-2-20000000022000000220000000000000000000000
χ3722222222-2-222-222-222222222-200000000-2-2-2-2-20000000000000000002222-2-200-2-200000000000000000000
χ3822222222-2-222-222-222222222-200000000-2-2-2-2-2000000000000000000-2-2-2-222002200000000000000000000
χ3922222222-2-222-222-2-2-2-2-2-2-2-2-2-200000000-2222200000000000000000022-2-2-2-2002200000000000000000000
χ4022222222-2-222-222-2-2-2-2-2-2-2-2-2-200000000-22222000000000000000000-2-2222200-2-200000000000000000000
χ41222-2-22-2-2-2-200200222−2−222−2−202i−2i2i−2i2-22-202−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i22−22−2000000000000
χ42222-2-22-2-2-2-200200222−2−222−2−202i−2i2i−2i-22-2202−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i2−22−22000000000000
χ43222-2-22-2-2-2-200200222−2−222−2−20−2i2i−2i2i2-22-202−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i22−22−2000000000000
χ44222-2-22-2-2-2-200200222−2−222−2−20−2i2i−2i2i-22-2202−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i2−22−22000000000000
χ45222-2-22-2-2-2-2002002−2−222−2−22202i−2i2i−2i2-22-20−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2−22−22000000000000
χ46222-2-22-2-2-2-2002002−2−222−2−22202i−2i2i−2i-22-220−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i22−22−2000000000000
χ47222-2-22-2-2-2-2002002−2−222−2−2220−2i2i−2i2i2-22-20−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2−22−22000000000000
χ48222-2-22-2-2-2-2002002−2−222−2−2220−2i2i−2i2i-22-220−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i22−22−2000000000000
χ4922-22-2-22-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i-2000000002−2i−2i2i2i0000000000000000002-22i−2i-2200−2i2i00000000000000000000
χ5022-22-2-22-22-2-2-2222-22i2i2i2i−2i−2i−2i−2i-2000000002−2i−2i2i2i000000000000000000-22−2i2i2-2002i−2i00000000000000000000
χ5122-22-2-22-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i-20000000022i2i−2i−2i0000000000000000002-2−2i2i-22002i−2i00000000000000000000
χ5222-22-2-22-22-2-2-2222-2−2i−2i−2i−2i2i2i2i2i-20000000022i2i−2i−2i000000000000000000-222i−2i2-200−2i2i00000000000000000000
χ5322-22-2-22-2-2222-2-2-2200000000-22i2i−2i−2i2i2i−2i−2i2000022-2-2-2-22200000000−2i2i000000−2i2i0000000000000000000000
χ5422-22-2-22-2-2222-2-2-2200000000-22i2i−2i−2i−2i−2i2i2i20000-2-22222-2-200000000−2i2i0000002i−2i0000000000000000000000
χ5522-22-2-22-2-2222-2-2-2200000000-2−2i−2i2i2i2i2i−2i−2i20000-2-22222-2-2000000002i−2i000000−2i2i0000000000000000000000
χ5622-22-2-22-2-2222-2-2-2200000000-2−2i−2i2i2i−2i−2i2i2i2000022-2-2-2-222000000002i−2i0000002i−2i0000000000000000000000
χ5722-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i202-2-222i−2i−2i2i0i2−i2−i2i2−2i2i2i−2i000022−2−2−2−222000000000000−i2i2i2−i22−2−22000000000000
χ5822-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i202-2-22−2i2i2i−2i0i2−i2−i2i22i−2i−2i2i0000−2−22222−2−2000000000000−i2i2i2−i2−222−2000000000000
χ5922-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i20-222-22i−2i−2i2i0i2−i2−i2i22i−2i−2i2i0000−2−22222−2−2000000000000i2−i2−i2i22−2−22000000000000
χ6022-2-22-2-222-200-2002i2i2−i2−i2−i2−i2i2i20-222-2−2i2i2i−2i0i2−i2−i2i2−2i2i2i−2i000022−2−2−2−222000000000000i2−i2−i2i2−222−2000000000000
χ6122-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i202-2-222i−2i−2i2i0−i2i2i2−i2−2i2i2i−2i0000−2−22222−2−2000000000000i2−i2−i2i2−222−2000000000000
χ6222-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i202-2-22−2i2i2i−2i0−i2i2i2−i22i−2i−2i2i000022−2−2−2−222000000000000i2−i2−i2i22−2−22000000000000
χ6322-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i20-222-22i−2i−2i2i0−i2i2i2−i22i−2i−2i2i000022−2−2−2−222000000000000−i2i2i2−i2−222−2000000000000
χ6422-2-22-2-222-200-2002−i2−i2i2i2i2i2−i2−i20-222-2−2i2i2i−2i0−i2i2i2−i2−2i2i2i−2i0000−2−22222−2−2000000000000−i2i2i2−i22−2−22000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000000040000000000000000000000000000000000000000000000000000
χ66444-4-44-4-44400-400-42222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ67444-4-44-4-44400-400-4−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ6844-44-4-44-44-4444-4-4-400000000400000000-40000000000000000000000000000000000000000000000000000
χ6944-4-44-4-44-4400400-42i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ7044-4-44-4-44-4400400-4−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ714-444-4-4-44000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000002i2−2i22i2−2i22-22-22-22-200000000000000000000000000000000
χ724-444-4-4-44000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000−2i22i2−2i22i2-22-22-22-2200000000000000000000000000000000
χ734-444-4-4-4400000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000002i2−2i22i2−2i2-22-22-22-2200000000000000000000000000000000
χ744-444-4-4-4400000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000−2i22i2−2i22i22-22-22-22-200000000000000000000000000000000
χ754-44-44-44-4004-404-400000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ764-44-44-44-4004-404-40000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ774-44-44-44-400-440-4404i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ784-44-44-44-400-440-440−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-40000000022−2222−22−2222−22220000000000000000002i2−2i2−2i22i2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ804-4-4444-4-40000000022−2222−22−2222−2222000000000000000000−2i22i22i2−2i22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ814-4-4444-4-400000000−2222−222222−2222−220000000000000000002i2−2i2−2i22i22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ824-4-4444-4-400000000−2222−222222−2222−22000000000000000000−2i22i22i2−2i2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ834-4-4-4-4444004-40-4404-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-4-4444004-40-440-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ854-4-4-4-444400-4404-4000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000
χ864-4-4-4-444400-4404-40000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000

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