Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8491 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8500 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#3546 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,29,31,25)(23,28)(24,27)(26,30,34,32)(33,35)(36,37,40,43,41,45,39,44)(38,46,47,42,48,50,49,51);(20,22)(21,25)(23,30)(24,31)(26,28)(27,29)(32,33)(34,35)(36,38)(37,42)(39,49)(40,47)(41,48)(43,50)(44,46)(45,51);(20,22)(21,26)(23,32)(24,31)(25,28)(27,34)(29,35)(30,33)(37,43)(39,40)(42,50)(44,45)(46,51)(47,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1488);