Finite Group Databasebeta

← Group #10692015

Character table — Group #10692015

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order1222344444444666121212122441212121212121212688888888122424242424242424242424242424242424661212244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ911111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1ii−i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-1-11ii−i−ii−i1-1
χ1011111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1ii−i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-111-1−i−iii−ii-11
χ1111111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1ii−i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii-11-1-1111-1-11−i−iiii−i-11
χ1211111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1ii−i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii-11-1-111-111-1ii−i−i−ii1-1
χ1311111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1−i−iiiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-11-1-1111-1-11ii−i−i−ii-11
χ1411111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1−i−iiiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-111-1−i−iiii−i1-1
χ1511111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1−i−iii−i−iii1−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-1-11−i−iii−ii1-1
χ1611111-1-111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1−i−iii−i−iii1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-111-1ii−i−ii−i-11
χ1722222222222-2-22222222-2-2-222-2-222-2-2-200000000-2000000000000000000000022-2-200000000
χ1822222222222-2-22222222-2-2-222-2-222-2-2-200000000-20000000000000000000000-2-22200000000
χ192222222-2-2-2-2222222222-22-2-2-222-2-222-200002-22-2-20000000022-2-222-2-2000000000000000000
χ202222222-2-2-2-2222222222-22-2-2-222-2-222-20000-22-22-200000000-2-222-2-222000000000000000000
χ212222222-2-2-2-2-2-222222222-22-2-2-2-2-2-2-2-22000000002000000000000000000000000002i−2i2i−2i0000
χ222222222-2-2-2-2-2-222222222-22-2-2-2-2-2-2-2-2200000000200000000000000000000000000−2i2i−2i2i0000
χ2322222-2-222-2-222222-2-2-2-22-2-222-2-2-2-222200000000-200000000000000000000002-22-200000000
χ2422222-2-222-2-222222-2-2-2-22-2-222-2-2-2-222200000000-20000000000000000000000-22-2200000000
χ2522222-2-2-2-22222222-2-2-2-2-2-22-2-2-2-22222-2000000002000000000000000000000000002-2-220000
χ2622222-2-2-2-22222222-2-2-2-2-2-22-2-2-2-22222-200000000200000000000000000000000000-222-20000
χ2722222-2-2-2-222-2-2222-2-2-2-222-2-2-22222-2-2200002i−2i−2i2i-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222-2-2-2-222-2-2222-2-2-2-222-2-2-22222-2-220000−2i2i2i−2i-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ302222-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ312222-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-22222-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ322222-122222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111111111111122-1-1-1-1000000000000
χ332222-122-2-2-2-222-1-1-1-1-1-1-1-22-211-1-111-1-1100002-22-21−i3−i3i3i3−i3−i3i3i3-1-111-1-11100−i3i3−i3i3000000000000
χ342222-122-2-2-2-222-1-1-1-1-1-1-1-22-211-1-111-1-1100002-22-21i3i3−i3−i3i3i3−i3−i3-1-111-1-11100i3−i3i3−i3000000000000
χ352222-122-2-2-2-222-1-1-1-1-1-1-1-22-211-1-111-1-110000-22-221−i3−i3i3i3−i3−i3i3i311-1-111-1-100i3−i3i3−i3000000000000
χ362222-122-2-2-2-222-1-1-1-1-1-1-1-22-211-1-111-1-110000-22-221i3i3−i3−i3i3i3−i3−i311-1-111-1-100−i3i3−i3i3000000000000
χ372222-1-2-222-2-2-2-2-1-1-11111-222-1-1-1-1111112i2i−2i−2i2i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii2-2-1-111000000000000
χ382222-1-2-222-2-2-2-2-1-1-11111-222-1-1-1-1111112i2i−2i−2i−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i-2211-1-1000000000000
χ392222-1-2-222-2-2-2-2-1-1-11111-222-1-1-1-111111−2i−2i2i2i2i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii-2211-1-1000000000000
χ402222-1-2-222-2-2-2-2-1-1-11111-222-1-1-1-111111−2i−2i2i2i−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i2-2-1-111000000000000
χ412222-1-2-2-2-222-2-2-1-1-1111122-211-1-1-1-111-100002i−2i−2i2i133−3−3−3−333−i−iiiii−i−i00−i3i3i3−i3000000000000
χ422222-1-2-2-2-222-2-2-1-1-1111122-211-1-1-1-111-100002i−2i−2i2i1−3−33333−3−3−i−iiiii−i−i00i3−i3−i3i3000000000000
χ432222-1-2-2-2-222-2-2-1-1-1111122-211-1-1-1-111-10000−2i2i2i−2i133−3−3−3−333ii−i−i−i−iii00i3−i3−i3i3000000000000
χ442222-1-2-2-2-222-2-2-1-1-1111122-211-1-1-1-111-10000−2i2i2i−2i1−3−33333−3−3ii−i−i−i−iii00−i3i3i3−i3000000000000
χ454444-2444444-4-4-2-2-2-2-2-2-2-4-4-4-2-222-2-22220000000020000000000000000000000000000000000
χ464444-244-4-4-4-4-4-4-2-2-2-2-2-2-24-4422222222-200000000-20000000000000000000000000000000000
χ474444-2-4-444-4-444-2-2-222224-4-4-2-22222-2-2-20000000020000000000000000000000000000000000
χ484444-2-4-4-4-44444-2-2-22222-4-442222-2-2-2-2200000000-20000000000000000000000000000000000
χ4944-4-440000004i−4i4-4-400000000000004i−4i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ5044-4-440000004i−4i4-4-400000000000004i−4i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ5144-4-44000000−4i4i4-4-40000000000000−4i4i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ5244-4-44000000−4i4i4-4-40000000000000−4i4i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ5344-4-4-20000004i−4i-2222323−23−2300000−2i32i300−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ500000000000000000000000000
χ5444-4-4-20000004i−4i-2222323−23−2300000−2i32i300−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ500000000000000000000000000
χ5544-4-4-20000004i−4i-222−23−232323000002i3−2i300−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ1300000000000000000000000000
χ5644-4-4-20000004i−4i-222−23−232323000002i3−2i300−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ1300000000000000000000000000
χ5744-4-4-2000000−4i4i-2222323−23−23000002i3−2i3002i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ700000000000000000000000000
χ5844-4-4-2000000−4i4i-2222323−23−23000002i3−2i3002i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ700000000000000000000000000
χ5944-4-4-2000000−4i4i-222−23−23232300000−2i32i3002i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ2300000000000000000000000000
χ6044-4-4-2000000−4i4i-222−23−23232300000−2i32i3002i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ2300000000000000000000000000
χ614-44-444i−4i4-44i−4i00-44-44i−4i4i−4i0004-4004i−4i0000000000000000000000000000000000000000000000
χ624-44-444i−4i-44−4i4i00-44-44i−4i4i−4i000-4400−4i4i0000000000000000000000000000000000000000000000
χ634-44-44−4i4i4-4−4i4i00-44-4−4i4i−4i4i0004-400−4i4i0000000000000000000000000000000000000000000000
χ644-44-44−4i4i-444i−4i00-44-4−4i4i−4i4i000-44004i−4i0000000000000000000000000000000000000000000000
χ654-44-4-24i−4i4-44i−4i002-22−2i2i−2i2i000-2200−2i2i00000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000
χ664-44-4-24i−4i4-44i−4i002-22−2i2i−2i2i000-2200−2i2i00000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000
χ674-44-4-24i−4i-44−4i4i002-22−2i2i−2i2i0002-2002i−2i00000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000
χ684-44-4-24i−4i-44−4i4i002-22−2i2i−2i2i0002-2002i−2i00000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000
χ694-44-4-2−4i4i4-4−4i4i002-222i−2i2i−2i000-22002i−2i00000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000
χ704-44-4-2−4i4i4-4−4i4i002-222i−2i2i−2i000-22002i−2i00000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000
χ714-44-4-2−4i4i-444i−4i002-222i−2i2i−2i0002-200−2i2i00000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000
χ724-44-4-2−4i4i-444i−4i002-222i−2i2i−2i0002-200−2i2i00000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000
χ738-8-88800000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-88-40000000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000
χ758-8-88-40000000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000

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