Finite Group Databasebeta

← Group #97548

Character table — Group #97548

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222222222224444444444444444444444448888888888888888888888884444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1
χ911-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-1ii−i−i
χ1011-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−i−iii
χ1111-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11-11−i−iii
χ1211-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-11-11ii−i−i
χ1311-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-11−i−iii
χ1411-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-1-11ii−i−i
χ1511-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-1ii−i−i
χ1611-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-1−i−iii
χ17222222222222222222-2-2-2-22-2-22-2-20000000022220000000000000000000000000000-2-20000
χ18222222222222222222-2-2-2-22-2-22-2-200000000-2-2-2-20000000000000000000000000000220000
χ192222222222222222-2-222-2-2-22-2-22-200002222000000000000000000000000000000-2-2000000
χ202222222222222222-2-222-2-2-22-2-22-20000-2-2-2-200000000000000000000000000000022000000
χ212222222222222222-2-2-2-222-2-22-2-22222200000000000000000000000000000000-2-200000000
χ222222222222222222-2-2-2-222-2-22-2-22-2-2-2-2000000000000000000000000000000002200000000
χ2322-2-2-2-2-2-2-2222222-222-2-2-2-2-222-2220000000022-2-20000000000000000000000000000-220000
χ2422-2-2-2-2-2-2-2222222-222-2-2-2-2-222-22200000000-2-22200000000000000000000000000002-20000
χ2522-2-2-2-2-2-2-2222222-2-2-222-2-22-222-22000022-2-2000000000000000000000000000000-22000000
χ2622-2-2-2-2-2-2-2222222-2-2-222-2-22-222-220000-2-2220000000000000000000000000000002-2000000
χ2722-2-2-2-2-2-2-2222222-2-2-2-2-22222-222-222-2-200000000000000000000000000000000-2200000000
χ2822-2-2-2-2-2-2-2222222-2-2-2-2-22222-222-2-2-222000000000000000000000000000000002-200000000
χ292-22222-2-2-222-22-2-2-200002-200-20022i−2i2i−2i0000000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000000000
χ302-22222-2-2-222-22-2-2-200002-200-20022i−2i2i−2i00000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000
χ312-22222-2-2-222-22-2-2-200002-200-2002−2i2i−2i2i0000000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000000000
χ322-22222-2-2-222-22-2-2-200002-200-2002−2i2i−2i2i00000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000000000
χ332-222-2-222-22-22-22-2-2002-2000-2002000002i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i20000000022−2−222−2−20000000000
χ342-222-2-222-22-22-22-2-2002-2000-2002000002i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i200000000−2−222−2−2220000000000
χ352-222-2-222-22-22-22-2-2002-2000-200200000−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i200000000−2−222−2−2220000000000
χ362-222-2-222-22-22-22-2-2002-2000-200200000−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i20000000022−2−222−2−20000000000
χ372-22-22-22-22-222-2-22-22-20000-200200000000002i−2i2i−2i000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000
χ382-22-22-22-22-222-2-22-22-20000-200200000000002i−2i2i−2i00000000−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000
χ392-22-22-22-22-222-2-22-22-20000-20020000000000−2i2i−2i2i000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000
χ402-22-22-22-22-222-2-22-22-20000-20020000000000−2i2i−2i2i00000000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000
χ412-2-22-22-22-2-222-2-2222-20000200-200000000002i−2i−2i2i00000000i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000
χ422-2-22-22-22-2-222-2-2222-20000200-200000000002i−2i−2i2i00000000−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000
χ432-2-22-22-22-2-222-2-2222-20000200-20000000000−2i2i2i−2i00000000i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000
χ442-2-22-22-22-2-222-2-2222-20000200-20000000000−2i2i2i−2i00000000−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000
χ452-2-2-222-2-222-22-22-22002-2000200-2000002i−2i−2i2i00002−22−2−22−2200000000−i2−i2i2i2i2i2−i2−i20000000000
χ462-2-2-222-2-222-22-22-22002-2000200-2000002i−2i−2i2i0000−22−222−22−200000000i2i2−i2−i2−i2−i2i2i20000000000
χ472-2-2-222-2-222-22-22-22002-2000200-200000−2i2i2i−2i00002−22−2−22−2200000000i2i2−i2−i2−i2−i2i2i20000000000
χ482-2-2-222-2-222-22-22-22002-2000200-200000−2i2i2i−2i0000−22−222−22−200000000−i2−i2i2i2i2i2−i2−i20000000000
χ492-2-2-2-2-222222-22-2-2200002-200200-22i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000000000
χ502-2-2-2-2-222222-22-2-2200002-200200-22i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000000000
χ512-2-2-2-2-222222-22-2-2200002-200200-2−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000
χ522-2-2-2-2-222222-22-2-2200002-200200-2−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000
χ534444-4-4-4-444-4-4-4-4440000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ544444-4-4-4-444-4-4-4-444000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ55444-44-4-44-4-44-4-44-44000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ56444-44-4-44-4-44-4-44-4400000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ57444-4-444-4-4-4-444-4-4400000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ58444-4-444-4-4-4-444-4-440000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ5944-444-4-444-4-444-4-4-400000000000000000000000000000000000000002-2-22-222-20000000000
χ6044-444-4-444-4-444-4-4-40000000000000000000000000000000000000000-222-22-2-220000000000
χ6144-44-444-44-44-4-44-4-4000000000000000000000000000000002-2-22-222-2000000000000000000
χ6244-44-444-44-44-4-44-4-400000000000000000000000000000000-222-22-2-22000000000000000000
χ6344-4-44444-44-4-4-4-44-40000000000000000000000002-2-22-222-200000000000000000000000000
χ6444-4-44444-44-4-4-4-44-4000000000000000000000000-222-22-2-2200000000000000000000000000
χ654-44444-4-4-444-44-4-4-40000-4400400-40000000000000000000000000000000000000000000000
χ664-444-4-444-44-44-44-4-400-44000400-400000000000000000000000000000000000000000000000
χ674-44-44-44-44-444-4-44-4-440000400-4000000000000000000000000000000000000000000000000
χ684-44-4-44-444-4-4-4444-40000000000000000000000000000000000000000000000000000002i−2i2i−2i
χ694-44-4-44-444-4-4-4444-4000000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ704-4-444-44-4-4-4-4-444440000000000000000000000000000000000000000000000000000002-2-22
χ714-4-444-44-4-4-4-4-44444000000000000000000000000000000000000000000000000000000-222-2
χ724-4-44-44-44-4-444-4-444-440000-4004000000000000000000000000000000000000000000000000
χ734-4-4-444-4-444-44-44-4400-44000-400400000000000000000000000000000000000000000000000
χ744-4-4-4-4-444444-44-4-440000-4400-40040000000000000000000000000000000000000000000000

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