Finite Group Databasebeta

← Group #142148

Character table — Group #142148

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order1222222244444488888888888824444444448888888888444444448888888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ101111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ121111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ131111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ19222222-2-22-22-222222222220000-2-200000000000000-2-2-2-20000000000000000i2−i2i2−i2i2−i2i2−i20000
χ20222222-2-22-22-222222222220000-2-200000000000000-2-2-2-20000000000000000−i2i2−i2i2−i2i2−i2i20000
χ21222222-2-22-22-222-2-2-2-2-2-2-2-20000-2-20000000000000022220000000000000000i2−i2i2−i2−i2i2−i2i20000
χ22222222-2-22-22-222-2-2-2-2-2-2-2-20000-2-20000000000000022220000000000000000−i2i2−i2i2i2−i2i2−i20000
χ23222222-2-2-22-22-2-2000000002222-220000000022-2-2-2-20000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ24222222-2-2-22-22-2-2000000002222-220000000022-2-2-2-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ25222222-2-2-22-22-2-200000000-2-2-2-2-2200000000-2-22222000022-2-222-2-200000000000000000000
χ26222222-2-2-22-22-2-200000000-2-2-2-2-2200000000-2-222220000-2-222-2-22200000000000000000000
χ272222-2-2222222-2-22222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ282222-2-2222222-2-2-2-2-2-222222222-2-22222-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000
χ292222-2-2-2-22-22-2-2-22222-2-2-2-200002200000000000000-2-22200000000000000002−2−222−2−220000
χ302222-2-2-2-22-22-2-2-22222-2-2-2-200002200000000000000-2-2220000000000000000−222−2−222−20000
χ312222-2-2-2-22-22-2-2-2-2-2-2-222220000220000000000000022-2-200000000000000002−2−22−222−20000
χ322222-2-2-2-22-22-2-2-2-2-2-2-222220000220000000000000022-2-20000000000000000−222−22−2−220000
χ332222-2-2-2-2-22-22220000000022222-200000000-2-222-2-200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ342222-2-2-2-2-22-22220000000022222-200000000-2-222-2-20000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ352222-2-2-2-2-22-222200000000-2-2-2-22-20000000022-2-22200000000000022-2-2-2-222000000000000
χ362222-2-2-2-2-22-222200000000-2-2-2-22-20000000022-2-222000000000000-2-22222-2-2000000000000
χ372-2-22002-2-222-20022-2-200002i2i−2i−2i0000002i2i−2i−2i00002i−2i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-2-22002-2-222-20022-2-200002i2i−2i−2i0000002i2i−2i−2i00002i−2i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-2-22002-2-222-20022-2-20000−2i−2i2i2i000000−2i−2i2i2i0000−2i2i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ402-2-22002-2-222-20022-2-20000−2i−2i2i2i000000−2i−2i2i2i0000−2i2i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ412-2-22002-2-222-200-2-22200002i2i−2i−2i000000−2i−2i2i2i00002i−2i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ422-2-22002-2-222-200-2-22200002i2i−2i−2i000000−2i−2i2i2i00002i−2i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ432-2-22002-2-222-200-2-2220000−2i−2i2i2i0000002i2i−2i−2i0000−2i2i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ442-2-22002-2-222-200-2-2220000−2i−2i2i2i0000002i2i−2i−2i0000−2i2i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ452-2-2200-2222-2-20000002i2i−2i−2i2i2i−2i−2i0022-2-200000000−2i2i002i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ462-2-2200-2222-2-20000002i2i−2i−2i2i2i−2i−2i0022-2-200000000−2i2i002i−2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ472-2-2200-2222-2-20000002i2i−2i−2i−2i−2i2i2i00-2-222000000002i−2i002i−2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ482-2-2200-2222-2-20000002i2i−2i−2i−2i−2i2i2i00-2-222000000002i−2i002i−2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ492-2-2200-2222-2-2000000−2i−2i2i2i2i2i−2i−2i00-2-22200000000−2i2i00−2i2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ502-2-2200-2222-2-2000000−2i−2i2i2i2i2i−2i−2i00-2-22200000000−2i2i00−2i2i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ512-2-2200-2222-2-2000000−2i−2i2i2i−2i−2i2i2i0022-2-2000000002i−2i00−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ522-2-2200-2222-2-2000000−2i−2i2i2i−2i−2i2i2i0022-2-2000000002i−2i00−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ5344444444-4-4-4-4-4-40000000000004-40000000000000000000000000000000000000000000000
χ544444-4-444-4-4-4-444000000000000-440000000000000000000000000000000000000000000000
χ5544-4-4000000004i−4i2i2−2i22i2−2i222−2222−2222−2222−22002-22-22i−2i2i−2i002i2−2i20000000000000000000000000000000000
χ5644-4-4000000004i−4i2i2−2i22i2−2i222−2222−22−2222−222200-22-22−2i2i−2i2i00−2i22i20000000000000000000000000000000000
χ5744-4-4000000004i−4i−2i22i2−2i22i2−2222−222222−2222−2200-22-22−2i2i−2i2i002i2−2i20000000000000000000000000000000000
χ5844-4-4000000004i−4i−2i22i2−2i22i2−2222−2222−2222−2222002-22-22i−2i2i−2i00−2i22i20000000000000000000000000000000000
χ5944-4-400000000−4i4i2i2−2i22i2−2i2−2222−222222−2222−2200-22-222i−2i2i−2i00−2i22i20000000000000000000000000000000000
χ6044-4-400000000−4i4i2i2−2i22i2−2i2−2222−2222−2222−2222002-22-2−2i2i−2i2i002i2−2i20000000000000000000000000000000000
χ6144-4-400000000−4i4i−2i22i2−2i22i222−2222−2222−2222−22002-22-2−2i2i−2i2i00−2i22i20000000000000000000000000000000000
χ6244-4-400000000−4i4i−2i22i2−2i22i222−2222−22−2222−222200-22-222i−2i2i−2i002i2−2i20000000000000000000000000000000000
χ634-44-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i2002-2-22-222-22i2−2i2000000000000000000000000000000000000
χ644-44-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i200-222-22-2-22−2i22i2000000000000000000000000000000000000
χ654-44-44-400000000−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i200-222-22-2-222i2−2i2000000000000000000000000000000000000
χ664-44-44-400000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2002-2-22-222-2−2i22i2000000000000000000000000000000000000
χ674-44-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i200-222-2-222-2−2i22i2000000000000000000000000000000000000
χ684-44-4-44000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i2002-2-222-2-222i2−2i2000000000000000000000000000000000000
χ694-44-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2002-2-222-2-22−2i22i2000000000000000000000000000000000000
χ704-44-4-4400000000−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i200-222-2-222-22i2−2i2000000000000000000000000000000000000
χ714-4-44004-44-4-440000004i4i−4i−4i0000000000000000000000−4i4i0000000000000000000000000000
χ724-4-44004-44-4-44000000−4i−4i4i4i00000000000000000000004i−4i0000000000000000000000000000
χ734-4-4400-44-4-4440044-4-4000000000000000000000000-44000000000000000000000000000000
χ744-4-4400-44-4-44400-4-4440000000000000000000000004-4000000000000000000000000000000

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