Finite Group Databasebeta

← Group #10705248

Character table — Group #10705248

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order122234444446668888881212121212122424242444444444161616162424484848484848484824888888121212122424242422441616161688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1
χ911111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1ii−i−i11iiii−i−i−i−i1-111-1-1i−i11-1-1ii−i−i11-1-1ii−i−ii−i
χ1011111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1−i−iii11−i−i−i−iiiii1-111-1-1−ii11-1-1−i−iii11-1-1−i−iii−ii
χ1111111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-111ii−i−i11iiii−i−i−i−i1-111-1-1−ii-1-111−i−iii-1-111ii−i−i−ii
χ1211111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-111−i−iii11−i−i−i−iiiii1-111-1-1i−i-1-111ii−i−i-1-111−i−iiii−i
χ1311111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1ii−i−i11iiii−i−i−i−i-11-1-111i−i11-1-1ii−i−i-1-111−i−iii−ii
χ1411111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1−i−iii11−i−i−i−iiiii-11-1-111−ii11-1-1−i−iii-1-111ii−i−ii−i
χ1511111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111ii−i−i11iiii−i−i−i−i-11-1-111−ii-1-111−i−iii11-1-1−i−iiii−i
χ1611111-1-111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111−i−iii11−i−i−i−iiiii-11-1-111i−i-1-111ii−i−i11-1-1ii−i−i−ii
χ1722222222222222-2-2-2-2-2-2222222-2-2-2-2222200000000-2-20000000022-2-2-2-200000000000000000000
χ1822222222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000-2-200000000-2-2222200000000000000000000
χ192222222-2-2-2-222200000022-2-2-2-2000022220000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2-2-2000000000000000000−i2i2−i2i200
χ202222222-2-2-2-222200000022-2-2-2-2000022220000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2-2-2000000000000000000i2−i2i2−i200
χ212222222-2-2-2-222200000022-2-2-2-20000-2-2-2-20000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i222000000000000000000i2−i2i2−i200
χ222222222-2-2-2-222200000022-2-2-2-20000-2-2-2-20000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i222000000000000000000−i2i2−i2i200
χ2322222-2-222-2-22222222-2-2-2-222-2-2222222-2-200000000-2-2000000002-2-2-22200000000000000000000
χ2422222-2-222-2-22222222-2-2-2-222-2-22222-2-22200000000-2-200000000-2222-2-200000000000000000000
χ2522222-2-2-2-222222000000-2-2-2-222000022-2-200002−2−220022−2−2−2−222-220000000000000000002−2−2200
χ2622222-2-2-2-222222000000-2-2-2-222000022-2-20000−222−200−2−22222−2−2-22000000000000000000−222−200
χ2722222-2-2-2-222222000000-2-2-2-2220000-2-22200002−2−220022−2−2−2−2222-2000000000000000000−222−200
χ2822222-2-2-2-222222000000-2-2-2-2220000-2-2220000−222−200−2−22222−2−22-20000000000000000002−2−2200
χ292222-1222222-1-1-1222222-1-1-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ302222-1222222-1-1-1222222-1-1-1-1-1-1-1-1-1-100002222-2-2-2-2-1-111111111000000-2-2-1-1-1-111110000000000
χ312222-1222222-1-1-1222222-1-1-1-1-1-1-1-1-1-10000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ322222-1222222-1-1-1222222-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-111111111000000221111-1-1-1-10000000000
χ332222-1-2-222-2-2-1-1-1-2-2-2-22211-1-1111111000022-2-22i2i−2i−2i-1-1−i−i−i−iiiii0000002i−2i-1-111−i−iii0000000000
χ342222-1-2-222-2-2-1-1-1-2-2-2-22211-1-1111111000022-2-2−2i−2i2i2i-1-1iiii−i−i−i−i000000−2i2i-1-111ii−i−i0000000000
χ352222-1-2-222-2-2-1-1-1-2-2-2-22211-1-11111110000-2-2222i2i−2i−2i-1-1−i−i−i−iiiii000000−2i2i11-1-1ii−i−i0000000000
χ362222-1-2-222-2-2-1-1-1-2-2-2-22211-1-11111110000-2-222−2i−2i2i2i-1-1iiii−i−i−i−i0000002i−2i11-1-1−i−iii0000000000
χ3722-2-222i−2i2-22i−2i-22-22i2i−2i−2i2-22i−2i2-22i−2i2i2i−2i−2i0000000000002-20000000000000000000000002-22i−2i000000
χ3822-2-222i−2i2-22i−2i-22-22i2i−2i−2i2-22i−2i2-22i−2i2i2i−2i−2i0000000000002-2000000000000000000000000-22−2i2i000000
χ3922-2-222i−2i2-22i−2i-22-2−2i−2i2i2i-222i−2i2-22i−2i−2i−2i2i2i00002-22i−2i0000-2200000000000000002-22i−2i00000000000000
χ4022-2-222i−2i2-22i−2i-22-2−2i−2i2i2i-222i−2i2-22i−2i−2i−2i2i2i0000-22−2i2i0000-220000000000000000-22−2i2i00000000000000
χ4122-2-22−2i2i2-2−2i2i-22-22i2i−2i−2i-22−2i2i2-2−2i2i2i2i−2i−2i00002-2−2i2i0000-2200000000000000002-2−2i2i00000000000000
χ4222-2-22−2i2i2-2−2i2i-22-22i2i−2i−2i-22−2i2i2-2−2i2i2i2i−2i−2i0000-222i−2i0000-220000000000000000-222i−2i00000000000000
χ4322-2-22−2i2i2-2−2i2i-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i−2i2i2i0000000000002-20000000000000000000000002-2−2i2i000000
χ4422-2-22−2i2i2-2−2i2i-22-2−2i−2i2i2i2-2−2i2i2-2−2i2i−2i−2i2i2i0000000000002-2000000000000000000000000-222i−2i000000
χ4522-2-2-12i−2i2-22i−2i1-11−2i−2i2i2i-22−ii-11−iiii−i−i00002-22i−2i00001-1ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000-11−iiζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ4622-2-2-12i−2i2-22i−2i1-11−2i−2i2i2i-22−ii-11−iiii−i−i00002-22i−2i00001-1−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000000-11−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ4722-2-2-12i−2i2-22i−2i1-11−2i−2i2i2i-22−ii-11−iiii−i−i0000-22−2i2i00001-1ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000001-1i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ4822-2-2-12i−2i2-22i−2i1-11−2i−2i2i2i-22−ii-11−iiii−i−i0000-22−2i2i00001-1−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000001-1i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ4922-2-2-1−2i2i2-2−2i2i1-112i2i−2i−2i-22i−i-11i−i−i−iii00002-2−2i2i00001-1−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000-11i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ5022-2-2-1−2i2i2-2−2i2i1-112i2i−2i−2i-22i−i-11i−i−i−iii00002-2−2i2i00001-1ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000-11i−iζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ5122-2-2-1−2i2i2-2−2i2i1-112i2i−2i−2i-22i−i-11i−i−i−iii0000-222i−2i00001-1−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000001-1−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ5222-2-2-1−2i2i2-2−2i2i1-112i2i−2i−2i-22i−i-11i−i−i−iii0000-222i−2i00001-1ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000001-1−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ534444-2444444-2-2-2-4-4-4-4-4-4-2-2-2-2-2-22222000000000000220000000000000000000000000000000000
χ544444-244-4-4-4-4-2-2-2000000-2-22222000000000000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ554444-244-4-4-4-4-2-2-2000000-2-222220000000000002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ564444-2-4-444-4-4-2-2-24444-4-422-2-222-2-2-2-2000000000000220000000000000000000000000000000000
χ574444-2-4-4-4-444-2-2-20000002222-2-200000000000022−22−222200−2−22222−2−200000000000000000000000000
χ584444-2-4-4-4-444-2-2-20000002222-2-2000000000000−222222−220022−2−2−2−22200000000000000000000000000
χ5944-4-444i−4i-44−4i4i-44-40000004i−4i-44−4i4i0000000000000000000000000000000000000000000000000000
χ6044-4-44−4i4i-444i−4i-44-4000000−4i4i-444i−4i0000000000000000000000000000000000000000000000000000
χ6144-4-4-24i−4i4-44i−4i2-224i4i−4i−4i4-4−2i2i-22−2i2i−2i−2i2i2i000000000000-220000000000000000000000000000000000
χ6244-4-4-24i−4i-44−4i4i2-22000000−2i2i2-22i−2i000000000000000000−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−ζ2200000000000000000000000000
χ6344-4-4-24i−4i-44−4i4i2-22000000−2i2i2-22i−2i000000000000000000ζ4+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+ζ2200000000000000000000000000
χ6444-4-4-2−4i4i4-4−4i4i2-22−4i−4i4i4i4-42i−2i-222i−2i2i2i−2i−2i000000000000-220000000000000000000000000000000000
χ6544-4-4-2−4i4i-444i−4i2-220000002i−2i2-2−2i2i000000000000000000−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+ζ2200000000000000000000000000
χ6644-4-4-2−4i4i-444i−4i2-220000002i−2i2-2−2i2i000000000000000000ζ4−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−ζ2200000000000000000000000000
χ674-44-44000000-4-44−2i22i2−2i22i200000000−2i22i2−2i22i24i−4i00000000000000000000000022−2200000000000000000000
χ684-44-44000000-4-44−2i22i2−2i22i200000000−2i22i2−2i22i2−4i4i000000000000000000000000−222200000000000000000000
χ694-44-44000000-4-442i2−2i22i2−2i2000000002i2−2i22i2−2i24i−4i000000000000000000000000−222200000000000000000000
χ704-44-44000000-4-442i2−2i22i2−2i2000000002i2−2i22i2−2i2−4i4i00000000000000000000000022−2200000000000000000000
χ714-4-4440000004-4-422−22−22220000000022−22−2222004i−4i00000000000000000000−2i22i20000000000000000000000
χ724-4-4440000004-4-422−22−22220000000022−22−222200−4i4i000000000000000000002i2−2i20000000000000000000000
χ734-4-4440000004-4-4−222222−2200000000−222222−22004i−4i000000000000000000002i2−2i20000000000000000000000
χ744-4-4440000004-4-4−222222−2200000000−222222−2200−4i4i00000000000000000000−2i22i20000000000000000000000
χ758-88-8-400000044-4−4i24i2−4i24i2000000002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ768-88-8-400000044-44i2−4i24i2−4i200000000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ778-8-88-4000000-44442−42−424200000000−222222−22000000000000000000000000000000000000000000000000
χ788-8-88-4000000-444−424242−420000000022−22−2222000000000000000000000000000000000000000000000000

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