Finite Group Databasebeta

← Group #481487

Character table — Group #481487

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222244444444888888888888888888888888881111111122224444444488888888888888888888888888
order12224444224422444444444444444444444444888888882222444422442244444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i111111111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-111-1-1-1-1111-111-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1111-111-1-111-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-111-1-111-1-1-1-1111-111-1-111-1-1-1-111-1-111-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1111-111-1-111-1-1-1-111-1-111-1-111-1-111
χ111111-1-1-1-111-1-111-1-1-1-1111-1-1-111-1-11111-1-111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1111-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ121111-1-1-1-111-1-111-1-1-1-1111-1-1-111-1-111-1-111-1-11111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1111-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ131111-1-1-1-111-1-1-1-11111-1-11-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-111-1-1-1-11111-1-11-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-111-1-1-1-11111-1-11-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-111-1-1-1-11111-1-11-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-111-1-1-1-11111-1-11-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i1111-1-1-1-111-1-1-1-11111-1-11-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111-1-1-1-11111-1-11-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii1111-1-1-1-111-1-1-1-11111-1-11-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222-2-2-2-2-2-20000000000000000000000002222222222222222-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-22222-2-2000000000000000000000000222222222222-2-2-2-22222-2-2000000000000000000000000
χ192222-2-2-2-222-2-222-2-222-2-2-220000000000000000000000002222-2-2-2-222-2-222-2-222-2-2-22000000000000000000000000
χ202222-2-2-2-222-2-2-2-222-2-222-220000000000000000000000002222-2-2-2-222-2-2-2-222-2-222-22000000000000000000000000
χ2122-2-222-2-22-22-22-22-200000000000000000000002−22−22−22−222-2-222-2-22-22-22-22-200000000000000000000002−22−22−22−2
χ2222-2-222-2-22-22-22-22-20000000000000000000000−22−22−22−2222-2-222-2-22-22-22-22-20000000000000000000000−22−22−22−22
χ2322-2-222-2-22-22-2-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i222-2-222-2-22-22-2-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ2422-2-222-2-22-22-2-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i222-2-222-2-22-22-2-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2522-2-222-2-2-22-2200002i−2i2i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000022-2-222-2-2-22-2200002i−2i2i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ2622-2-222-2-2-22-2200002i−2i2i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000022-2-222-2-2-22-2200002i−2i2i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ2722-2-222-2-2-22-220000−2i2i−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000022-2-222-2-2-22-220000−2i2i−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ2822-2-222-2-2-22-220000−2i2i−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000022-2-222-2-2-22-220000−2i2i−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ2922-2-2-2-2222-2-222-2-2200000000000000000000002−2−222−2−2222-2-2-2-2222-2-222-2-2200000000000000000000002−2−222−2−22
χ3022-2-2-2-2222-2-222-2-220000000000000000000000−222−2−222−222-2-2-2-2222-2-222-2-220000000000000000000000−222−2−222−2
χ3122-2-2-2-2222-2-22-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i222-2-2-2-2222-2-22-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ3222-2-2-2-2222-2-22-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i222-2-2-2-2222-2-22-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3322-2-2-2-222-222-200002i−2i−2i2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000022-2-2-2-222-222-200002i−2i−2i2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ3422-2-2-2-222-222-200002i−2i−2i2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000022-2-2-2-222-222-200002i−2i−2i2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ3522-2-2-2-222-222-20000−2i2i2i−2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000022-2-2-2-222-222-20000−2i2i2i−2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ3622-2-2-2-222-222-20000−2i2i2i−2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000022-2-2-2-222-222-20000−2i2i2i−2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ3744444444-4-4-4-4000000000000000000000000000000000044444444-4-4-4-40000000000000000000000000000000000
χ384444-4-4-4-4-4-44400000000000000000000000000000000004444-4-4-4-4-4-4440000000000000000000000000000000000
χ394-44-44i−4i4i−4i000000000000002-22i−2i000000000000000000004-44-44i−4i4i−4i000000000000002-22i−2i00000000000000000000
χ404-44-44i−4i4i−4i00000000000000-22−2i2i000000000000000000004-44-44i−4i4i−4i00000000000000-22−2i2i00000000000000000000
χ414-44-4−4i4i−4i4i000000000000002-2−2i2i000000000000000000004-44-4−4i4i−4i4i000000000000002-2−2i2i00000000000000000000
χ424-44-4−4i4i−4i4i00000000000000-222i−2i000000000000000000004-44-4−4i4i−4i4i00000000000000-222i−2i00000000000000000000
χ434-4-444i−4i−4i4i0000000000000000002i−2i2-200000000000000004-4-444i−4i−4i4i0000000000000000002i−2i2-20000000000000000
χ444-4-444i−4i−4i4i000000000000000000−2i2i-2200000000000000004-4-444i−4i−4i4i000000000000000000−2i2i-220000000000000000
χ454-4-44−4i4i4i−4i0000000000000000002i−2i-2200000000000000004-4-44−4i4i4i−4i0000000000000000002i−2i-220000000000000000
χ464-4-44−4i4i4i−4i000000000000000000−2i2i2-200000000000000004-4-44−4i4i4i−4i000000000000000000−2i2i2-20000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ48111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ491111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ51111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ52111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ53111111111111-1-1-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ54111111111111-1-1-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ551111-1-1-1-111-1-111-1-1-1-1111-111-1-111-1-111-1-111-1-111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-11-1-111-1-111-1-111-1-111-1-111-1-111
χ561111-1-1-1-111-1-111-1-1-1-1111-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-111-1-11111-1-1-11-1-111-1-11111-1-111-1-111-1-111-1-1
χ571111-1-1-1-111-1-111-1-1-1-1111-1-1-111-1-11111-1-111-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111-1-1-1111-1-111-1-1-1-111-1-11111-1-111-1-1
χ581111-1-1-1-111-1-111-1-1-1-1111-1-1-111-1-111-1-111-1-11111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1111-1-111-1-111-1-111-1-1-1-111-1-111
χ591111-1-1-1-111-1-1-1-11111-1-11-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-11111-1-11111-1-1-1-111-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ601111-1-1-1-111-1-1-1-11111-1-11-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-11111-1-11111-1-1-1-111-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ611111-1-1-1-111-1-1-1-11111-1-11-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-11111-1-11111-1-1-1-111-1111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ621111-1-1-1-111-1-1-1-11111-1-11-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-11111-1-11111-1-1-1-111-1111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ632222222222222222-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ64222222222222-2-2-2-22222-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222000000000000000000000000
χ652222-2-2-2-222-2-222-2-222-2-2-22000000000000000000000000-2-2-2-22222-2-222-2-222-2-2222-2000000000000000000000000
χ662222-2-2-2-222-2-2-2-222-2-222-22000000000000000000000000-2-2-2-22222-2-22222-2-222-2-22-2000000000000000000000000
χ6722-2-222-2-22-22-22-22-200000000000000000000002−22−22−22−2-2-222-2-222-22-22-22-220000000000000000000000−22−22−22−22
χ6822-2-222-2-22-22-22-22-20000000000000000000000−22−22−22−22-2-222-2-222-22-22-22-2200000000000000000000002−22−22−22−2
χ6922-2-222-2-22-22-2-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2-2-222-2-222-22-222-22-20000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ7022-2-222-2-22-22-2-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2-2-222-2-222-22-222-22-20000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ7122-2-222-2-2-22-2200002i−2i2i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000-2-222-2-2222-22-20000−2i2i−2i2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ7222-2-222-2-2-22-2200002i−2i2i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000-2-222-2-2222-22-20000−2i2i−2i2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ7322-2-222-2-2-22-220000−2i2i−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000-2-222-2-2222-22-200002i−2i2i−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ7422-2-222-2-2-22-220000−2i2i−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000-2-222-2-2222-22-200002i−2i2i−2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ7522-2-2-2-2222-2-222-2-2200000000000000000000002−2−222−2−22-2-22222-2-2-222-2-222-20000000000000000000000−222−2−222−2
χ7622-2-2-2-2222-2-222-2-220000000000000000000000−222−2−222−2-2-22222-2-2-222-2-222-200000000000000000000002−2−222−2−22
χ7722-2-2-2-2222-2-22-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i2-2-22222-2-2-222-22-2-220000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ7822-2-2-2-2222-2-22-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i2-2-22222-2-2-222-22-2-220000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ7922-2-2-2-222-222-200002i−2i−2i2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000-2-22222-2-22-2-220000−2i2i2i−2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ8022-2-2-2-222-222-200002i−2i−2i2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000-2-22222-2-22-2-220000−2i2i2i−2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ8122-2-2-2-222-222-20000−2i2i2i−2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000-2-22222-2-22-2-2200002i−2i−2i2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ8222-2-2-2-222-222-20000−2i2i2i−2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000-2-22222-2-22-2-2200002i−2i−2i2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ8344444444-4-4-4-40000000000000000000000000000000000-4-4-4-4-4-4-4-444440000000000000000000000000000000000
χ844444-4-4-4-4-4-4440000000000000000000000000000000000-4-4-4-4444444-4-40000000000000000000000000000000000
χ854-44-44i−4i4i−4i000000000000002-22i−2i00000000000000000000-44-44−4i4i−4i4i00000000000000-22−2i2i00000000000000000000
χ864-44-44i−4i4i−4i00000000000000-22−2i2i00000000000000000000-44-44−4i4i−4i4i000000000000002-22i−2i00000000000000000000
χ874-44-4−4i4i−4i4i000000000000002-2−2i2i00000000000000000000-44-444i−4i4i−4i00000000000000-222i−2i00000000000000000000
χ884-44-4−4i4i−4i4i00000000000000-222i−2i00000000000000000000-44-444i−4i4i−4i000000000000002-2−2i2i00000000000000000000
χ894-4-444i−4i−4i4i0000000000000000002i−2i2-20000000000000000-444-4−4i4i4i−4i000000000000000000−2i2i-220000000000000000
χ904-4-444i−4i−4i4i000000000000000000−2i2i-220000000000000000-444-4−4i4i4i−4i0000000000000000002i−2i2-20000000000000000
χ914-4-44−4i4i4i−4i0000000000000000002i−2i-220000000000000000-444-44i−4i−4i4i000000000000000000−2i2i2-20000000000000000
χ924-4-44−4i4i4i−4i000000000000000000−2i2i2-20000000000000000-444-44i−4i−4i4i0000000000000000002i−2i-220000000000000000

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