Finite Group Databasebeta

← Group #68262

Character table — Group #68262

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222224444444444444444444888888888881212242424242448
order122234444666121212124448888121212122424242424242424488121212122424242444224884
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-111111-1-1-1
χ41111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1111
χ51111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ61111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11
χ71111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-11
χ81111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-111-1
χ9222222-22-2222222200-20000-2-2-2-200000000000000000002200-2000
χ10222222-22-2222222200-20000-2-2-2-20000000000000000000-2-2002000
χ1122222-22-22222-2-2-2-222-2000022-2-200000000-20022-2-2000000000000
χ1222222-22-22222-2-2-2-2-2-2-2000022-2-200000000200-2-222000000000000
χ1322222-2-2-2-2222-2-2-2-20020000-2-2220000000000000000000002-20000
χ1422222-2-2-2-2222-2-2-2-20020000-2-222000000000000000000000-220000
χ152222-12222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-100000000
χ162222-12222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1111111112-2-2-1-1-1-1111100000000
χ172222-12222-1-1-1-1-1-1-1-2-222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111111100000000
χ182222-12222-1-1-1-1-1-1-1-2-22-2-2-2-2-1-1-1-111111111-2221111-1-1-1-100000000
χ192222-1-22-22-1-1-1111122-20000-1-1113333−3−3−3−3-200-1-11133−3−300000000
χ202222-1-22-22-1-1-1111122-20000-1-111−3−3−3−33333-200-1-111−3−33300000000
χ212222-1-22-22-1-1-11111-2-2-20000-1-1113333−3−3−3−320011-1-1−3−33300000000
χ222222-1-22-22-1-1-11111-2-2-20000-1-111−3−3−3−3333320011-1-133−3−300000000
χ2322-2-22-20202-2-2-2-222000−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2000000000002i−2i0002−20
χ2422-2-22-20202-2-2-2-222000−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i200000000000−2i2i000−220
χ2522-2-22-20202-2-2-2-222000i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2000000000002i−2i000−220
χ2622-2-22-20202-2-2-2-222000i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i200000000000−2i2i0002−20
χ272-2-222020-2-22-200002i−2i02−22−22-2002−22−22−22−20−i2i22i−2i00−i2i2−i2i200000000
χ282-2-222020-2-22-200002i−2i0−22−222-200−22−22−22−220i2−i22i−2i00i2−i2i2−i200000000
χ292-2-222020-2-22-20000−2i2i02−22−22-2002−22−22−22−20i2−i2−2i2i00i2−i2i2−i200000000
χ302-2-222020-2-22-20000−2i2i0−22−222-200−22−22−22−220−i2i2−2i2i00−i2i2−i2i200000000
χ312-2-22-1020-21-113−33−32i−2i02−22−2-113−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230−i2i2−ii−i3i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ322-2-22-1020-21-113−33−32i−2i0−22−22-113−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230i2−i2−ii−i3i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ332-2-22-1020-21-113−33−3−2i2i02−22−2-113−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230i2−i2i−ii3−i3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ342-2-22-1020-21-113−33−3−2i2i0−22−22-113−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230−i2i2i−ii3−i3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ352-2-22-1020-21-11−33−332i−2i02−22−2-11−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70−i2i2−iii3−i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ362-2-22-1020-21-11−33−332i−2i0−22−22-11−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70i2−i2−iii3−i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ372-2-22-1020-21-11−33−33−2i2i02−22−2-11−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70i2−i2i−i−i3i3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ382-2-22-1020-21-11−33−33−2i2i0−22−22-11−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70−i2i2i−i−i3i3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ394444-24-44-4-2-2-2-2-2-2-200-400002222000000000000000000000000000
χ404444-2-4-4-4-4-2-2-22222004000022-2-2000000000000000000000000000
χ4144-4-4440-404-4-444-4-400000000000000000000000000000000000000
χ4244-4-4-240-40-222-2-22200000000000i6i6−i6−i6−i6−i6i6i60000000000000000000
χ4344-4-4-240-40-222-2-22200000000000−i6−i6i6i6i6i6−i6−i60000000000000000000
χ4444-4-4-2-4040-22222-2-2000−2i2−2i22i22i20000i2i2−i2−i2i2i2−i2−i20000000000000000000
χ4544-4-4-2-4040-22222-2-20002i22i2−2i2−2i20000−i2−i2i2i2−i2−i2i2i20000000000000000000
χ464-44-440000-4-4400000002i−2i−2i2i00002i−2i−2i2i2i−2i−2i2i0000000000000000000
χ474-44-440000-4-440000000−2i2i2i−2i0000−2i2i2i−2i−2i2i2i−2i0000000000000000000
χ484-44-4-2000022-223−23−23230002i−2i−2i2i0000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000
χ494-44-4-2000022-223−23−2323000−2i2i2i−2i0000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000
χ504-44-4-2000022-2−232323−230002i−2i−2i2i0000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000
χ514-44-4-2000022-2−232323−23000−2i2i2i−2i0000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000
χ524-4-4440-404-44-400000000000-4400000000000000000000000000000
χ534-4-44-20-4042-2223−2323−2300000002-2−2323000000000000000000000000000
χ544-4-44-20-4042-22−2323−232300000002-223−23000000000000000000000000000

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