Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10766 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #379 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | C22⋊#95 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1180 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)(22,31)(23,35,37,28)(24,39)(25,29)(26,30)(27,33)(32,46,48,45)(34,43)(36,44,38,50)(40,42)(41,47,49,51);(20,22,25,33,26,34,24,40)(21,27,29,43,30,42,39,31)(23,32,38,47,37,48,36,51)(28,41,44,46,35,49,50,45);(20,23)(21,28)(22,32)(24,36)(25,38)(26,37)(27,41)(29,44)(30,35)(31,45)(33,47)(34,48)(39,50)(40,51)(42,49)(43,46)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3754);