Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#26857 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C4×C4⋊C4×C19 ◁ G | |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,26)(22,27,23,25)(28,29)(30,33)(31,32)(34,35)(37,40)(41,43);(20,22,24,23)(21,25,26,27)(37,41)(39,42)(40,43);(20,23,24,22)(21,25,26,27)(29,32)(33,35)(36,37)(38,40)(39,43)(41,42);(21,26)(25,27)(28,30,31,34)(29,33,32,35)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19845);