Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#9893 |
| 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 | |
388 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)(20,21)(22,26)(23,24)(25,27)(29,32,33,34)(36,37,40,43,41,44,39,49)(38,45,48,50,46,51,47,42);(21,24)(25,26)(28,29,30,34,31,33,35,32)(36,38)(37,42,44,50)(39,47)(40,48)(41,46)(43,45,49,51);(20,22,23,27)(21,25,24,26)(38,46)(42,50)(45,51)(47,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2881);