Finite Group Databasebeta

← Group #10692421

Character table — Group #10692421

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888888888161616161616242424242424242448484848
order122234444666121212122444466888812121212121288888812122424242424242424242424242424242424661212224488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-11111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ911111-1-1-1-1111-1-1-1-1-111-11-1-1ii−i−i1111-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-11-1ii−i−ii−i1-1
χ1011111-1-1-1-1111-1-1-1-1-111-11-1-1ii−i−i1111-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-11-11−i−iii−ii-11
χ1111111-1-1-1-1111-1-1-1-1-111-11-1-1ii−i−i1111-1-1−i−iiii−i1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-1111-11-1ii−i−i−ii-11
χ1211111-1-1-1-1111-1-1-1-1-111-11-1-1ii−i−i1111-1-1−i−iiii−i1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-11-11−i−iiii−i1-1
χ1311111-1-1-1-1111-1-1-1-1-111-11-1-1−i−iii1111-1-1ii−i−i−ii1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-1111-11-1−i−iiii−i-11
χ1411111-1-1-1-1111-1-1-1-1-111-11-1-1−i−iii1111-1-1ii−i−i−ii1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111-11-11ii−i−i−ii1-1
χ1511111-1-1-1-1111-1-1-1-1-111-11-1-1−i−iii1111-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-11-1−i−iii−ii1-1
χ1611111-1-1-1-1111-1-1-1-1-111-11-1-1−i−iii1111-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-11-11ii−i−ii−i-11
χ172222222222222222-22-2-2-2-2-2222222-2-2220000-2-2-2-20000000022-2-222-2-2000000000000000000
χ182222222222222222-22-2-2-2-2-2-2-2-2-222-2-222000022-2-200000000-2-222-2-222000000000000000000
χ192222222-2-222222222-22-2-2220000-2-222-2-2000000-2-2000000000000000000000000002i−2i2i−2i0000
χ202222222-2-222222222-22-2-2220000-2-222-2-2000000-2-200000000000000000000000000−2i2i−2i2i0000
χ212222222-2-22222222-2-2-222-2-20000-2-2-2-2-2-200000022000000000000000000000022-2-200000000
χ222222222-2-22222222-2-2-222-2-20000-2-2-2-2-2-2000000220000000000000000000000-2-22200000000
χ2322222-2-222222-2-2-2-22-2-2-22220000-2-2-2-2220000002-200000000000000000000002-2-2200000000
χ2422222-2-222222-2-2-2-22-2-2-22220000-2-2-2-2220000002-20000000000000000000000-222-200000000
χ2522222-2-222222-2-2-2-2-2-222-2-2-20000-2-22222000000-22000000000000000000000000002-2-220000
χ2622222-2-222222-2-2-2-2-2-222-2-2-20000-2-22222000000-2200000000000000000000000000-222-20000
χ2722222-2-2-2-2222-2-2-2-222-22-2222i2i−2i−2i22-2-2-2-20000−2i2i-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222-2-2-2-2222-2-2-2-222-22-222−2i−2i2i2i22-2-2-2-200002i−2i-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-12222-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ302222-12222-1-1-1-1-1-1-122222-1-12222-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ312222-12222-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ322222-12222-1-1-1-1-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ332222-12222-1-1-1-1-1-1-1-22-2-2-2112222-1-111-1-10000-2-211−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ342222-12222-1-1-1-1-1-1-1-22-2-2-2112222-1-111-1-10000-2-211i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ352222-12222-1-1-1-1-1-1-1-22-2-2-211-2-2-2-2-1-111-1-100002211−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ362222-12222-1-1-1-1-1-1-1-22-2-2-211-2-2-2-2-1-111-1-100002211i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ372222-1-2-2-2-2-1-1-1111122-22-2-1-12i2i−2i−2i-1-111110000−2i2i1-133−3−3−3−333−i−iiiii−i−i00−i3i3i3−i3000000000000
χ382222-1-2-2-2-2-1-1-1111122-22-2-1-12i2i−2i−2i-1-111110000−2i2i1-1−3−33333−3−3−i−iiiii−i−i00i3−i3−i3i3000000000000
χ392222-1-2-2-2-2-1-1-1111122-22-2-1-1−2i−2i2i2i-1-1111100002i−2i1-133−3−3−3−333ii−i−i−i−iii00i3−i3−i3i3000000000000
χ402222-1-2-2-2-2-1-1-1111122-22-2-1-1−2i−2i2i2i-1-1111100002i−2i1-1−3−33333−3−3ii−i−i−i−iii00−i3i3i3−i3000000000000
χ412222-1-2-2-2-2-1-1-11111-222-22112i2i−2i−2i-1-1-1-1112i2i−2i−2i2i−2i-11−i−i−i−iiiii−i−i−i−iiiii2-2-1-111000000000000
χ422222-1-2-2-2-2-1-1-11111-222-22112i2i−2i−2i-1-1-1-111−2i−2i2i2i2i−2i-11iiii−i−i−i−i−i−i−i−iiiii-2211-1-1000000000000
χ432222-1-2-2-2-2-1-1-11111-222-2211−2i−2i2i2i-1-1-1-1112i2i−2i−2i−2i2i-11−i−i−i−iiiiiiiii−i−i−i−i-2211-1-1000000000000
χ442222-1-2-2-2-2-1-1-11111-222-2211−2i−2i2i2i-1-1-1-111−2i−2i2i2i−2i2i-11iiii−i−i−i−iiiii−i−i−i−i2-2-1-111000000000000
χ454444-244-4-4-2-2-2-2-2-2-24-44-4-4-2-2000022-2-222000000220000000000000000000000000000000000
χ464444-244-4-4-2-2-2-2-2-2-2-4-4-444220000222222000000-2-20000000000000000000000000000000000
χ474444-2-4-444-2-2-222224-4-4-44-2-200002222-2-2000000-220000000000000000000000000000000000
χ484444-2-4-444-2-2-22222-4-444-422000022-2-2-2-20000002-20000000000000000000000000000000000
χ4944-4-44004i−4i4-4-400000000000000000004i−4i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ5044-4-44004i−4i4-4-400000000000000000004i−4i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ5144-4-4400−4i4i4-4-40000000000000000000−4i4i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ5244-4-4400−4i4i4-4-40000000000000000000−4i4i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ5344-4-4-2004i−4i-22223−2323−2300000000000−2i32i300−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ500000000000000000000000000
χ5444-4-4-2004i−4i-22223−2323−2300000000000−2i32i300−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ500000000000000000000000000
χ5544-4-4-2004i−4i-222−2323−2323000000000002i3−2i300−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ1300000000000000000000000000
χ5644-4-4-2004i−4i-222−2323−2323000000000002i3−2i300−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ1300000000000000000000000000
χ5744-4-4-200−4i4i-22223−2323−23000000000002i3−2i3002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ700000000000000000000000000
χ5844-4-4-200−4i4i-22223−2323−23000000000002i3−2i3002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ700000000000000000000000000
χ5944-4-4-200−4i4i-222−2323−232300000000000−2i32i3002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ2300000000000000000000000000
χ6044-4-4-200−4i4i-222−2323−232300000000000−2i32i3002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ2300000000000000000000000000
χ614-44-444-400-4-4444-4-40000000−2i22i2−2i22i20000000000000000000000−2i22i200−2i22i200000000000000000000
χ624-44-444-400-4-4444-4-400000002i2−2i22i2−2i200000000000000000000002i2−2i2002i2−2i200000000000000000000
χ634-44-44-4400-4-44-4-444000000022−22−2222000000000000000000000022−2200−222200000000000000000000
χ644-44-44-4400-4-44-4-4440000000−222222−220000000000000000000000−22220022−2200000000000000000000
χ654-44-4-24-40022-2-2-22200000−2i32i3−2i22i2−2i22i200−2i32i3000000000000000000i2−i26−6i2−i26−6000000000000000000
χ664-44-4-24-40022-2-2-22200000−2i32i32i2−2i22i2−2i200−2i32i3000000000000000000−i2i2−66−i2i2−66000000000000000000
χ674-44-4-24-40022-2-2-222000002i3−2i3−2i22i2−2i22i2002i3−2i3000000000000000000i2−i2−66i2−i2−66000000000000000000
χ684-44-4-24-40022-2-2-222000002i3−2i32i2−2i22i2−2i2002i3−2i3000000000000000000−i2i26−6−i2i26−6000000000000000000
χ694-44-4-2-440022-222-2-200000−2i32i322−22−2222002i3−2i3000000000000000000−22−i6i62−2i6−i6000000000000000000
χ704-44-4-2-440022-222-2-200000−2i32i3−222222−22002i3−2i30000000000000000002−2i6−i6−22−i6i6000000000000000000
χ714-44-4-2-440022-222-2-2000002i3−2i322−22−222200−2i32i3000000000000000000−22i6−i62−2−i6i6000000000000000000
χ724-44-4-2-440022-222-2-2000002i3−2i3−222222−2200−2i32i30000000000000000002−2−i6i6−22i6−i6000000000000000000
χ738-8-8880000-88-8000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-400004-4443−43−434300000000000000000000000000000000000000000000000000000000000
χ758-8-88-400004-44−434343−4300000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.