Finite Group Databasebeta

← Group #10692407

Character table — Group #10692407

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888888888888888161616161616242424242424242448484848
order122234444666121212122444488881212121212121212688888812242424242424242424242424242424244412121212244488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-11111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-11111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ911111-1-1-1-1111-1-1-1-1-111-11ii−i−i1111-1-1-1-1-1ii−i−ii−i1iiii−i−i−i−iiiii−i−i−i−i1-111-1-111-1-1ii−i−ii−i1-1
χ1011111-1-1-1-1111-1-1-1-1-111-11ii−i−i1111-1-1-1-1-1ii−i−ii−i1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-1-111−i−iii−ii-11
χ1111111-1-1-1-1111-1-1-1-1-111-11ii−i−i1111-1-1-1-1-1−i−iiii−i1−i−i−i−iiiiiiiii−i−i−i−i-11-1-11111-1-1ii−i−i−ii-11
χ1211111-1-1-1-1111-1-1-1-1-111-11ii−i−i1111-1-1-1-1-1−i−iiii−i1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-1-111−i−iiii−i1-1
χ1311111-1-1-1-1111-1-1-1-1-111-11−i−iii1111-1-1-1-1-1ii−i−i−ii1iiii−i−i−i−i−i−i−i−iiiii-11-1-11111-1-1−i−iiii−i-11
χ1411111-1-1-1-1111-1-1-1-1-111-11−i−iii1111-1-1-1-1-1ii−i−i−ii1iiii−i−i−i−i−i−i−i−iiiii-11-1-111-1-111ii−i−i−ii1-1
χ1511111-1-1-1-1111-1-1-1-1-111-11−i−iii1111-1-1-1-1-1−i−iii−ii1−i−i−i−iiiii−i−i−i−iiiii1-111-1-111-1-1−i−iii−ii1-1
χ1611111-1-1-1-1111-1-1-1-1-111-11−i−iii1111-1-1-1-1-1−i−iii−ii1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-1-111ii−i−ii−i-11
χ172222222222222222-22-2-2-2222222-2-2-2-222-20000-2-2-20000000022-2-222-2-2000000000000000000
χ182222222222222222-22-2-2-2-2-2-2-222-2-2-2-222-2000022-200000000-2-222-2-222000000000000000000
χ192222222-2-222222222-2-2-220000-2-2-2-2-2-2-2-22000000200000000000000000000002-22-200000000
χ202222222-2-222222222-2-2-220000-2-2-2-2-2-2-2-2200000020000000000000000000000-22-2200000000
χ212222222-2-22222222-2-222-20000-2-22222-2-2-2000000-2000000000000000000000000002i−2i2i−2i0000
χ222222222-2-22222222-2-222-20000-2-22222-2-2-2000000-200000000000000000000000000−2i2i−2i2i0000
χ2322222-2-222222-2-2-2-22-22-2-20000-2-222-2-2222000000-2000000000000000000000000002-2-220000
χ2422222-2-222222-2-2-2-22-22-2-20000-2-222-2-2222000000-200000000000000000000000000-222-20000
χ2522222-2-222222-2-2-2-2-2-2-2220000-2-2-2-22222-2000000200000000000000000000002-2-2200000000
χ2622222-2-222222-2-2-2-2-2-2-2220000-2-2-2-22222-200000020000000000000000000000-222-200000000
χ2722222-2-2-2-2222-2-2-2-222-22-22i2i−2i−2i22-2-222-2-220000−2i2i-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222-2-2-2-2222-2-2-2-222-22-2−2i−2i2i2i22-2-222-2-2200002i−2i-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-12222-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ302222-12222-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-2-2-2-222-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ312222-12222-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ322222-12222-1-1-1-1-1-1-122222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1111111111111111122-1-1-1-1000000000000
χ332222-12222-1-1-1-1-1-1-1-22-2-2-22222-1-11111-1-110000-2-21−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ342222-12222-1-1-1-1-1-1-1-22-2-2-22222-1-11111-1-110000-2-21i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ352222-12222-1-1-1-1-1-1-1-22-2-2-2-2-2-2-2-1-11111-1-110000221−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ362222-12222-1-1-1-1-1-1-1-22-2-2-2-2-2-2-2-1-11111-1-110000221i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ372222-1-2-2-2-2-1-1-1111122-22-22i2i−2i−2i-1-111-1-111-10000−2i2i133−3−3−3−333−i−iiiii−i−i00−i3i3i3−i3000000000000
χ382222-1-2-2-2-2-1-1-1111122-22-22i2i−2i−2i-1-111-1-111-10000−2i2i1−3−33333−3−3−i−iiiii−i−i00i3−i3−i3i3000000000000
χ392222-1-2-2-2-2-1-1-1111122-22-2−2i−2i2i2i-1-111-1-111-100002i−2i133−3−3−3−333ii−i−i−i−iii00i3−i3−i3i3000000000000
χ402222-1-2-2-2-2-1-1-1111122-22-2−2i−2i2i2i-1-111-1-111-100002i−2i1−3−33333−3−3ii−i−i−i−iii00−i3i3i3−i3000000000000
χ412222-1-2-2-2-2-1-1-11111-222-222i2i−2i−2i-1-1-1-1111112i2i−2i−2i2i−2i-1−i−i−i−iiiii−i−i−i−iiiii2-2-1-111000000000000
χ422222-1-2-2-2-2-1-1-11111-222-222i2i−2i−2i-1-1-1-111111−2i−2i2i2i2i−2i-1iiii−i−i−i−i−i−i−i−iiiii-2211-1-1000000000000
χ432222-1-2-2-2-2-1-1-11111-222-22−2i−2i2i2i-1-1-1-1111112i2i−2i−2i−2i2i-1−i−i−i−iiiiiiiii−i−i−i−i-2211-1-1000000000000
χ442222-1-2-2-2-2-1-1-11111-222-22−2i−2i2i2i-1-1-1-111111−2i−2i2i2i−2i2i-1iiii−i−i−i−iiiii−i−i−i−i2-2-1-111000000000000
χ454444-244-4-4-2-2-2-2-2-2-24-4-4-44000022222222-2000000-20000000000000000000000000000000000
χ464444-244-4-4-2-2-2-2-2-2-2-4-444-4000022-2-2-2-222200000020000000000000000000000000000000000
χ474444-2-4-444-2-2-222224-44-4-4000022-2-222-2-2-200000020000000000000000000000000000000000
χ484444-2-4-444-2-2-22222-4-4-44400002222-2-2-2-22000000-20000000000000000000000000000000000
χ494-44-44004i−4i-44-400000000000000000004i−4i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ504-44-44004i−4i-44-400000000000000000004i−4i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ514-44-4400−4i4i-44-40000000000000000000−4i4i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ524-44-4400−4i4i-44-40000000000000000000−4i4i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ534-44-4-2004i−4i2-222323−23−23000000000−2i32i30000−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ500000000000000000000000000
χ544-44-4-2004i−4i2-222323−23−23000000000−2i32i30000−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ500000000000000000000000000
χ554-44-4-2004i−4i2-22−23−2323230000000002i3−2i30000−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ1300000000000000000000000000
χ564-44-4-2004i−4i2-22−23−2323230000000002i3−2i30000−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ1300000000000000000000000000
χ574-44-4-200−4i4i2-222323−23−230000000002i3−2i300002i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ700000000000000000000000000
χ584-44-4-200−4i4i2-222323−23−230000000002i3−2i300002i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ700000000000000000000000000
χ594-44-4-200−4i4i2-22−23−232323000000000−2i32i300002i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ2300000000000000000000000000
χ604-44-4-200−4i4i2-22−23−232323000000000−2i32i300002i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ2300000000000000000000000000
χ614-4-4444i−4i00-4-444i−4i4i−4i000002+2i−2−2i2−2i−2+2i0000000000000000000000002+2i−2−2i002−2i−2+2i00000000000000000000
χ624-4-4444i−4i00-4-444i−4i4i−4i00000−2−2i2+2i−2+2i2−2i000000000000000000000000−2−2i2+2i00−2+2i2−2i00000000000000000000
χ634-4-444−4i4i00-4-44−4i4i−4i4i000002−2i−2+2i2+2i−2−2i0000000000000000000000002−2i−2+2i002+2i−2−2i00000000000000000000
χ644-4-444−4i4i00-4-44−4i4i−4i4i00000−2+2i2−2i−2−2i2+2i000000000000000000000000−2+2i2−2i00−2−2i2+2i00000000000000000000
χ654-4-44-24i−4i0022-2−2i2i−2i2i000002+2i−2−2i2−2i−2+2i00−2i32i323−23000000000000000000−1−i1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−1+i1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000
χ664-4-44-24i−4i0022-2−2i2i−2i2i000002+2i−2−2i2−2i−2+2i002i3−2i3−2323000000000000000000−1−i1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−1+i1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000
χ674-4-44-24i−4i0022-2−2i2i−2i2i00000−2−2i2+2i−2+2i2−2i00−2i32i323−230000000000000000001+i−1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ221−i−1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000
χ684-4-44-24i−4i0022-2−2i2i−2i2i00000−2−2i2+2i−2+2i2−2i002i3−2i3−23230000000000000000001+i−1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ221−i−1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000
χ694-4-44-2−4i4i0022-22i−2i2i−2i000002−2i−2+2i2+2i−2−2i00−2i32i3−2323000000000000000000−1+i1−i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−1−i1+i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000
χ704-4-44-2−4i4i0022-22i−2i2i−2i000002−2i−2+2i2+2i−2−2i002i3−2i323−23000000000000000000−1+i1−iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−1−i1+iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000
χ714-4-44-2−4i4i0022-22i−2i2i−2i00000−2+2i2−2i−2−2i2+2i00−2i32i3−23230000000000000000001−i−1+iζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ221+i−1−iζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000
χ724-4-44-2−4i4i0022-22i−2i2i−2i00000−2+2i2−2i−2−2i2+2i002i3−2i323−230000000000000000001−i−1+i−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ221+i−1−i−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000
χ7388-8-8800008-8-8000000000000000000000000000000000000000000000000000000000000000
χ7488-8-8-40000-444−4i34i34i3−4i300000000000000000000000000000000000000000000000000000000000
χ7588-8-8-40000-4444i3−4i3−4i34i300000000000000000000000000000000000000000000000000000000000

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