Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C42 |
| direct product | C19×#21826 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C42×C19 ◁ G | |
1050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37)(38,44,46,41)(39,42)(40,43)(45,50,51,48)(47,49);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,38)(37,41)(39,45)(40,46)(42,48)(43,44)(47,51)(49,50);(21,27)(25,28)(26,35)(33,34)(36,39,40,47)(37,42,43,49)(38,45,46,51)(41,48,44,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14814);