Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12945 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #447 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,37)(27,31)(28,46)(29,47)(30,36)(32,39)(33,42)(34,45)(35,44)(38,51)(40,50)(41,53)(43,52)(48,49)(54,55);(20,22,23,21)(25,31)(27,42)(28,45)(29,44)(32,49)(33,35)(34,36)(37,51)(38,39)(40,48)(43,55)(46,47)(50,52)(53,54);(24,26)(25,32)(27,43)(28,38)(29,48)(30,41)(31,49)(33,53)(34,50)(35,54)(36,52)(37,46)(39,45)(40,44)(42,55)(47,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5933);