Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#7733 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C43×C19 ◁ G | |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29,31,33,32,30,34,35)(36,37)(38,44,46,41)(39,47)(40,43)(42,48)(45,49,51,50);(20,21,23,25)(22,27,26,24)(28,30)(29,32)(31,33)(34,35)(36,38,40,46)(37,41,43,44)(39,45,48,51)(42,49,47,50);(29,30)(33,35)(36,39,40,48)(37,42,43,47)(38,45,46,51)(41,49,44,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 721);