Finite Group Databasebeta

← Group #11711232

Character table — Group #11711232

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size112223333336666666666666666632323232323232324848484848484848
order12488224444444444488888888883612122424242444448888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1
χ4111-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111
χ52222222222222222222222222222-1-1-1-1-1-1-1-100000000
χ6222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-1-1-1-1111100000000
χ722-20022222222-2-2-2-2-2000000000022-2-2000000000000
χ822-20022222222-2-2-2-2-20000000000-1-11133−3−300000000
χ922-20022222222-2-2-2-2-20000000000-1-111−3−33300000000
χ102-202−22-222-2-22-2000002−22222−2−2−2−22-2002−22−200000000
χ112-202−22-222-2-22-2000002−22222−2−2−2−2-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ122-202−22-222-2-22-2000002−22222−2−2−2−2-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ132-20−222-222-2-22-200000−22−2−2−2−222222-200−22−2200000000
χ142-20−222-222-2-22-200000−22−2−2−2−22222-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ152-20−222-222-2-22-200000−22−2−2−2−22222-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ163333333-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-1000000001111-1-1-1-1
χ173333333-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-1-100000000-1-1-1-11111
χ1833333-1-1−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i-1-1-111−1+2i−1−2i11−1+2i−1−2i0000000011-1-1i−ii−i
χ1933333-1-1−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i-1-1-111−1+2i−1−2i11−1+2i−1−2i00000000-1-111−ii−ii
χ2033333-1-1−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i-1-1-111−1−2i−1+2i11−1−2i−1+2i0000000011-1-1−ii−ii
χ2133333-1-1−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i-1-1-111−1−2i−1+2i11−1−2i−1+2i00000000-1-111i−ii−i
χ22333-3-333-1-1-1-1-1-1-1-1-1-13-3-311111111000000001-11-1-1-111
χ23333-3-333-1-1-1-1-1-1-1-1-1-13-3-31111111100000000-11-1111-1-1
χ24333-3-3-1-1−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i-111-1-11−2i1+2i-1-11−2i1+2i000000001-1-11i−i−ii
χ25333-3-3-1-1−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i-111-1-11−2i1+2i-1-11−2i1+2i00000000-111-1−iii−i
χ26333-3-3-1-1−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i-111-1-11+2i1−2i-1-11+2i1−2i000000001-1-11−iii−i
χ27333-3-3-1-1−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i-111-1-11+2i1−2i-1-11+2i1−2i00000000-111-1i−i−ii
χ2866666-2-22222-2-2-2-222-2-2-2-2-222-2-2220000000000000000
χ29666-6-6-2-22222-2-2-2-222-22222-2-222-2-20000000000000000
χ3066-60066-2-2-2-2-2-22222-600000000000000000000000000
χ3166-600-2-22222-2-222-2-22004-4004-4000000000000000000
χ3266-600-2-22222-2-222-2-2200-4400-44000000000000000000
χ3366-600-2-2−2+4i−2−4i−2+4i−2−4i22-2-22−4i2+4i200000000000000000000000000
χ3466-600-2-2−2−4i−2+4i−2−4i−2+4i22-2-22+4i2−4i200000000000000000000000000
χ356-6032−326-6-2-222-220000032−32−2−2−2−222220000000000000000
χ366-6032−32-2222-2-2-224-4000−222−3222−232−2−20000000000000000
χ376-6032−32-2222-2-2-22-44000−22−3222232−2−2−20000000000000000
χ386-6032−32-22−2+4i−2−4i2−4i2+4i2-200000−22223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ23−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ230000000000000000
χ396-6032−32-22−2−4i−2+4i2+4i2−4i2-200000−2222−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ23−2−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ230000000000000000
χ406-60−32326-6-2-222-2200000−32322222−2−2−2−20000000000000000
χ416-60−3232-2222-2-2-224-40002−2−232−2−22−32220000000000000000
χ426-60−3232-2222-2-2-22-440002−232−2−2−2−322220000000000000000
χ436-60−3232-22−2+4i−2−4i2−4i2+4i2-2000002−2−2−2−3ζ5−ζ7−3ζ13−ζ23ζ5+3ζ7+ζ13+3ζ23223ζ5+ζ7+3ζ13+ζ23−ζ5−3ζ7−ζ13−3ζ230000000000000000
χ446-60−3232-22−2−4i−2+4i2+4i2−4i2-2000002−2−2−2ζ5+3ζ7+ζ13+3ζ23−3ζ5−ζ7−3ζ13−ζ2322−ζ5−3ζ7−ζ13−3ζ233ζ5+ζ7+3ζ13+ζ230000000000000000

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