Finite Group Databasebeta

← Group #10833336

Character table — Group #10833336

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222444444448888888888888888888888121212121212121216161616161616161624242424242424244848
order1222223444466666668888121212122244444488121212122424242424242424222244444661212121212122444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11-1
χ411111111111111111111111111-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-111-11
χ511111111111111111111-1-1111111-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-111-1-111-1-1111-1-111-1-1-1-1-1-11111-11
χ611111111111111111111-1-1111111-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-111111-1-111-1-11111-1-1-1-11-1
χ711111111111111111111-1-11111-1-11111-1-11-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-111-111-111-1-1-1-1
χ811111111111111111111-1-11111-1-11111-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-11111
χ9111111111111111111-1-111111111-1-111-1-1-11-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1111-1-11-1-111-1-1
χ10111111111111111111-1-111111111-1-111-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-111-111-111-1-111
χ11111111111111111111-1-1111111-1-111-1-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-11-1-11111-1-11111-1-1-1-1-11
χ12111111111111111111-1-1111111-1-111-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1111-1-11111-1-1-1-1-1-111111-1
χ13111111111111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-1-111-1-1-1111-1
χ14111111111111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-11111-1-1-1-11-1-1111-1-1-11
χ15111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ16111111111111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-1-1-1-1-10000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-100000000-2111111110000000000
χ19222222-12222-1-1-1-1-1-1-122-2-2-1-1-1-122-2-2-2-2-2-22-21111-1-1-1-11111000000002-1-111-1-1110000000000
χ20222222-12222-1-1-1-1-1-1-122-2-2-1-1-1-1-2-22222-2-22-21111-1-1-1-1111100000000-211-1-111-1-10000000000
χ21222222-12222-1-1-1-1-1-1-1-2-222-1-1-1-122-2-222-2-2-2211111111-1-1-1-100000000-2-1-11111-1-10000000000
χ22222222-12222-1-1-1-1-1-1-1-2-222-1-1-1-1-2-222-2-2-2-2-2211111111-1-1-1-100000000211-1-1-1-1110000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12222-2-222-2-2-1-1-1-11111111100000000-2-1-1-1-111110000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-22222-2-2-1-1-1-1111111110000000021111-1-1-1-10000000000
χ252222-2-222-2-222-2-2-2-22200222-22-2000000000-20000000022-2-22200-2-200000000000-2002000000
χ262222-2-222-2-222-2-2-2-22200222-22-2000000000-20000000022-2-2-2-2002200000000000200-2000000
χ272222-2-222-2-222-2-2-2-22200-2-22-22-2000000000200000000-2-2222200-2-200000000000200-2000000
χ282222-2-222-2-222-2-2-2-22200-2-22-22-2000000000200000000-2-222-2-2002200000000000-2002000000
χ292222-2-22-222-22-2-2-2-2222200-22-2200000000-20000022-2-20000002200-2-200000000002-20000000
χ302222-2-22-222-22-2-2-2-2222200-22-2200000000-20000022-2-2000000-2-200220000000000-220000000
χ312222-2-22-222-22-2-2-2-222-2-200-22-2200000000200000-2-2220000002200-2-20000000000-220000000
χ322222-2-22-222-22-2-2-2-222-2-200-22-2200000000200000-2-222000000-2-2002200000000002-20000000
χ332-2-222-2222-2-2-222-2-2-22000022-2-2002i−2i000000000000000000002-2002-20002i−2i000000002i−2i0000
χ342-2-222-2222-2-2-222-2-2-22000022-2-2002i−2i00000000000000000000-2200-220002i−2i00000000−2i2i0000
χ352-2-222-2222-2-2-222-2-2-22000022-2-200−2i2i000000000000000000002-2002-2000−2i2i00000000−2i2i0000
χ362-2-222-2222-2-2-222-2-2-22000022-2-200−2i2i00000000000000000000-2200-22000−2i2i000000002i−2i0000
χ372-2-222-22-2-222-222-2-2-220000-2-2222-2000000000000000000002-2002-20002-20000000000002-200
χ382-2-222-22-2-222-222-2-2-220000-2-2222-200000000000000000000-2200-220002-2000000000000-2200
χ392-2-222-22-2-222-222-2-2-220000-2-222-22000000000000000000002-2002-2000-22000000000000-2200
χ402-2-222-22-2-222-222-2-2-220000-2-222-2200000000000000000000-2200-22000-220000000000002-200
χ412-2-22-222-22-22-2-2-222-220000-222-200002-200000000000000002-22-2-22-2200000002-20000000000
χ422-2-22-222-22-22-2-2-222-220000-222-200002-20000000000000000-22-222-22-200000002-20000000000
χ432-2-22-222-22-22-2-2-222-220000-222-20000-2200000000000000002-2-22-222-20000000-220000000000
χ442-2-22-222-22-22-2-2-222-220000-222-20000-220000000000000000-222-22-2-220000000-220000000000
χ454444444-4-4-4-444444440000-4-4-4-40000000000000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000000000−2i3−2i32i32i300000000000000000000000000000000000
χ47444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000002i32i3−2i3−2i300000000000000000000000000000000000
χ484444-4-4-24-4-44-22222-2-20044-22-22000000000-400000000-2-222000000000000000000000000000
χ494444-4-4-24-4-44-22222-2-200-4-4-22-2200000000040000000022-2-2000000000000000000000000000
χ504444-4-4-2-444-4-22222-2-244002-22-200000000-400000-2-2220000000000000000000000000000000
χ514444-4-4-2-444-4-22222-2-2-4-4002-22-20000000040000022-2-20000000000000000000000000000000
χ524-44-40040000-400004-4−2i22i2−2i22i200000000002-2002-22-2−2i22i200−2i22i200000000000000000000000000000
χ534-44-40040000-400004-4−2i22i22i2−2i20000000000-2200-22-22−2i22i2002i2−2i200000000000000000000000000000
χ544-44-40040000-400004-42i2−2i2−2i22i20000000000-2200-22-222i2−2i200−2i22i200000000000000000000000000000
χ554-44-40040000-400004-42i2−2i22i2−2i200000000002-2002-22-22i2−2i2002i2−2i200000000000000000000000000000
χ564-44-400-200002−2i32i3−2i32i3-22−2i22i2−2i22i200000000002-200−1−i31+i3−1+i31−i3i2−i26−6i2−i26−6000000000000000000000000000
χ574-44-400-200002−2i32i3−2i32i3-22−2i22i22i2−2i20000000000-22001+i3−1−i31−i3−1+i3i2−i26−6−i2i2−66000000000000000000000000000
χ584-44-400-200002−2i32i3−2i32i3-222i2−2i2−2i22i20000000000-22001+i3−1−i31−i3−1+i3−i2i2−66i2−i26−6000000000000000000000000000
χ594-44-400-200002−2i32i3−2i32i3-222i2−2i22i2−2i200000000002-200−1−i31+i3−1+i31−i3−i2i2−66−i2i2−66000000000000000000000000000
χ604-44-400-2000022i3−2i32i3−2i3-22−2i22i2−2i22i200000000002-200−1+i31−i3−1−i31+i3i2−i2−66i2−i2−66000000000000000000000000000
χ614-44-400-2000022i3−2i32i3−2i3-22−2i22i22i2−2i20000000000-22001−i3−1+i31+i3−1−i3i2−i2−66−i2i26−6000000000000000000000000000
χ624-44-400-2000022i3−2i32i3−2i3-222i2−2i2−2i22i20000000000-22001−i3−1+i31+i3−1−i3−i2i26−6i2−i2−66000000000000000000000000000
χ634-44-400-2000022i3−2i32i3−2i3-222i2−2i22i2−2i200000000002-200−1+i31−i3−1−i31+i3−i2i26−6−i2i26−6000000000000000000000000000
χ644-4-444-4-244-4-42-2-2222-20000-2-222004i−4i00000000000000000000000000000−2i2i00000000000000
χ654-4-444-4-244-4-42-2-2222-20000-2-22200−4i4i000000000000000000000000000002i−2i00000000000000
χ664-4-444-4-2-4-4442-2-2222-2000022-2-24-400000000000000000000000000000-220000000000000000
χ674-4-444-4-2-4-4442-2-2222-2000022-2-2-44000000000000000000000000000002-20000000000000000
χ684-4-44-4444-44-4-4-4-444-4400004-4-440000000000000000000000000000000000000000000000000
χ694-4-44-44-24-44-4222-2-22-20000-222-200000000000000000000000000000000000−2i32i3000000000000
χ704-4-44-44-24-44-4222-2-22-20000-222-2000000000000000000000000000000000002i3−2i3000000000000
χ714-4-44-44-2-44-44222-2-22-200002-2-2200004-40000000000000000000000000000000-220000000000
χ724-4-44-44-2-44-44222-2-22-200002-2-220000-4400000000000000000000000000000002-20000000000
χ7388-8-8008000080000-8-8000000000000000000000000000000000000000000000000000000000
χ7488-8-800-40000-4−4i34i34i3−4i344000000000000000000000000000000000000000000000000000000000
χ7588-8-800-40000-44i3−4i3−4i34i344000000000000000000000000000000000000000000000000000000000

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