Finite Group Databasebeta

← Group #72266655

Character table — Group #72266655

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11113333444412121212242448484848969696969696969696969696969696969696256256256256256256256256256256256256256256256256
order1244224422442244242244444444444488888888336666661212121212121212
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32
χ31111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32
χ422222222-2-2-2-2-2-2-2-2222222-2-20000000000000000-1-11111-1-111-1-111-1-1
χ522222222-2-2-2-2-2-2-2-2222222-2-200000000000000001+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ622222222-2-2-2-2-2-2-2-2222222-2-200000000000000001−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ7333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ8333333333333333333-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ9333333333333333333-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-10000000000000000
χ10333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-10000000000000000
χ11333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133330000000000000000
χ1244-4-444-4-444-4-444-4-44-4000000000000000000000011111111-1-1-1-1-1-1-1-1
χ1344-4-444-4-444-4-444-4-44-40000000000000000000000−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32
χ1444-4-444-4-444-4-444-4-44-40000000000000000000000−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32
χ1544-4-444-4-4-4-444-4-4444-4000000000000000000000011-1-1-1-11111-1-111-1-1
χ1644-4-444-4-4-4-444-4-4444-40000000000000000000000−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ1744-4-444-4-4-4-444-4-4444-40000000000000000000000−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ184-44i−4i4-44i−4i4-44i−4i00000000000000002-22i−2i00000000111-11-1-1-1i−ii−ii−ii−i
χ194-44i−4i4-44i−4i4-44i−4i00000000000000002-22i−2i00000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32ζ22−ζ22ζ22−ζ22ζ14−ζ14ζ14−ζ14
χ204-44i−4i4-44i−4i4-44i−4i00000000000000002-22i−2i00000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32ζ14−ζ14ζ14−ζ14ζ22−ζ22ζ22−ζ22
χ214-4−4i4i4-4−4i4i4-4−4i4i00000000000000002-2−2i2i00000000111-11-1-1-1−ii−ii−ii−ii
χ224-4−4i4i4-4−4i4i4-4−4i4i00000000000000002-2−2i2i00000000−1−i32−1+i32−1−i321+i32−1+i321−i321+i321−i32−ζ22ζ22−ζ22ζ22−ζ14ζ14−ζ14ζ14
χ234-4−4i4i4-4−4i4i4-4−4i4i00000000000000002-2−2i2i00000000−1+i32−1−i32−1+i321−i32−1−i321+i321−i321+i32−ζ14ζ14−ζ14ζ14−ζ22ζ22−ζ22ζ22
χ2466666666-6-6-6-6-6-6-6-666-2-2-2-22200000000000000000000000000000000
χ2566-6-666-6-666-6-6-2-222-2222-2-22-222-2-222-2-2000000000000000000000000
χ2666-6-666-6-666-6-6-2-222-2222-2-22-2-2-222-2-222000000000000000000000000
χ2766-6-666-6-666-6-6-2-222-22-2-222-2222-2-2-2-222000000000000000000000000
χ2866-6-666-6-666-6-6-2-222-22-2-222-22-2-22222-2-2000000000000000000000000
χ2966-6-666-6-6-6-66622-2-2-2222-2-2-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ3066-6-666-6-6-6-66622-2-2-2222-2-2-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ3166-6-666-6-6-6-66622-2-2-22-2-2222-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ3266-6-666-6-6-6-66622-2-2-22-2-2222-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ338-88i−8i8-88i−8i-88−8i8i0000000000000000000000000000-1-11-11-111i−i−iii−i−ii
χ348-88i−8i8-88i−8i-88−8i8i00000000000000000000000000001+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32ζ22−ζ22−ζ22ζ22ζ14−ζ14−ζ14ζ14
χ358-88i−8i8-88i−8i-88−8i8i00000000000000000000000000001−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32ζ14−ζ14−ζ14ζ14ζ22−ζ22−ζ22ζ22
χ368-8−8i8i8-8−8i8i-888i−8i0000000000000000000000000000-1-11-11-111−iii−i−iii−i
χ378-8−8i8i8-8−8i8i-888i−8i00000000000000000000000000001+i321−i32−1−i321+i32−1+i321−i32−1−i32−1+i32−ζ22ζ22ζ22−ζ22−ζ14ζ14ζ14−ζ14
χ388-8−8i8i8-8−8i8i-888i−8i00000000000000000000000000001−i321+i32−1+i321−i32−1−i321+i32−1+i32−1−i32−ζ14ζ14ζ14−ζ14−ζ22ζ22ζ22−ζ22
χ39121212121212121212121212-4-4-4-4-4-400000000000000000000000000000000000000
χ401212121212121212-12-12-12-124444-4-400000000000000000000000000000000000000
χ4112-1212i−12i12-1212i−12i12-1212i−12i0000000000000000-22−2i2i000000000000000000000000
χ4212-1212i−12i-44−4i4i00004-44i−4i000000002-22i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ4312-1212i−12i-44−4i4i00004-44i−4i000000002-22i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ4412-1212i−12i-44−4i4i00004-44i−4i00000000-22−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ4512-1212i−12i-44−4i4i00004-44i−4i00000000-22−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ4612-12−12i12i12-12−12i12i12-12−12i12i0000000000000000-222i−2i000000000000000000000000
χ4712-12−12i12i-444i−4i00004-4−4i4i000000002-2−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ4812-12−12i12i-444i−4i00004-4−4i4i000000002-2−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ4912-12−12i12i-444i−4i00004-4−4i4i00000000-222i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ5012-12−12i12i-444i−4i00004-4−4i4i00000000-222i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ5124242424-8-8-8-800000000004-44-40000000000000000000000000000000000
χ5224242424-8-8-8-80000000000-44-440000000000000000000000000000000000
χ532424-24-24-8-88800000000004-4-440000000000000000000000000000000000
χ542424-24-24-8-8880000000000-444-40000000000000000000000000000000000
χ5524-2424i−24i-88−8i8i0000-88−8i8i0000000000000000000000000000000000000000
χ5624-24−24i24i-888i−8i0000-888i−8i0000000000000000000000000000000000000000

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