Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10757 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | C22⋊#95 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1168 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)(20,21,24,30,26,29,25,38)(22,27,33,41,32,40,37,42)(23,28,35,43,34,44,36,49)(31,45,47,51,46,39,48,50);(20,22,25,33,26,32,24,37)(21,27,30,42,29,40,38,41)(23,31,36,47,34,46,35,48)(28,39,43,51,44,45,49,50);(20,23)(21,28)(22,31)(24,35)(25,36)(26,34)(27,39)(29,44)(30,43)(32,46)(33,47)(37,48)(38,49)(40,45)(41,50)(42,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3745);