Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24 |
| direct product | C2×C19×#1394 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #99 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C22×Q8 | C23×C19 |
| prime radical | C24×C19 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C19 ◁ C23×Q8×C19 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(7,8,10,14,11,15,19,22)(9,13,16,21,17,12,18,20);(3,4,5,6)(8,12,15,13)(14,21,22,20)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5572);