Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#12579 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#99 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| socle | C2×C19 | C2×#342 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C22×#41×C19 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,24,29,26,31,25,30)(22,32,35,48,33,47,36,49)(23,37,38,46,39,28,40,44)(27,41,43,34,42,51,45,50);(20,22,25,36,26,33,24,35)(21,27,30,43,31,42,29,45)(23,34,38,51,39,50,40,41)(28,32,44,49,37,47,46,48);(22,33)(27,42)(32,47)(34,50)(35,36)(41,51)(43,45)(48,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5567);