Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#7586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C2×C19×#121 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26,27,24)(23,25)(29,33,34,35)(36,37,39,41,40,43,38,42);(20,22)(21,24)(23,27)(25,26)(28,29)(30,33)(31,35)(32,34)(37,41)(38,39)(42,43);(21,25)(24,26)(28,30,32,31)(29,33,34,35)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 574);