Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#10955 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | #1437 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
900 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)(20,21,24,31,26,29,25,30)(22,27,34,42,33,43,39,41)(23,35,37,28,36,44,38,45)(32,46,47,40,48,49,50,51);(20,22,25,34,26,33,24,39)(21,27,31,41,29,43,30,42)(23,32,38,47,36,48,37,50)(28,40,44,46,45,51,35,49);(20,23,26,36)(21,28)(22,32,33,48)(24,37,25,38)(27,40)(29,45)(30,35)(31,44)(34,47,39,50)(41,46)(42,49)(43,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3943);