Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C29 |
| direct product | C19×#34211 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
3102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,27,26)(28,29)(30,31)(32,40)(33,34)(35,38)(36,41)(37,42)(39,43);(24,26,27,25)(29,34)(31,35)(36,40)(39,42);(20,21,22,23)(28,30)(29,35)(31,34)(32,37)(33,38)(36,42)(39,40)(41,43);(28,31,33,35)(29,30,34,38)(32,39,41,42)(36,37,40,43);(28,32,33,41)(29,36,34,40)(30,37,38,43)(31,39,35,42)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27199);