Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11159 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #397 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1440 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
804 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)(20,21,25,29,26,31,24,30)(22,32,34,27,35,43,40,44)(23,36,38,46,39,45,41,28)(33,42,49,47,37,50,48,51);(20,22)(21,27)(23,37)(24,40)(25,34)(26,35)(28,42)(29,43)(30,32)(31,44)(33,39)(36,47)(38,48)(41,49)(45,51)(46,50);(20,23,24,38,26,39,25,41)(21,28,29,45,31,46,30,36)(22,33,34,48,35,37,40,49)(27,42,32,47,44,50,43,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4147);