Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#22841 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C23×C19 | C23×C4 |
| prime radical | C22×D4×C19 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(21,25)(26,27)(28,29)(30,33)(31,35)(32,34)(36,37,39,43,40,42,46,49)(38,41,45,48,44,47,50,51);(20,21,24,25)(22,26,23,27)(28,30,32,31)(29,33,34,35)(38,44)(41,47)(45,50)(48,51);(20,22,24,23)(21,26,25,27)(28,31,32,30)(29,33,34,35)(36,38)(37,41)(39,45)(40,44)(42,47)(43,48)(46,50)(49,51);(20,23,24,22)(21,26,25,27)(37,42)(38,44)(43,49)(45,50)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15829);