Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#9635 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | #389 |
| prime radical | C23×C19 | #125 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
260 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,24,27,25,28,23,32)(22,29,30,26,31,34,33,35)(37,42)(38,45)(39,40)(43,46)(44,49)(47,48);(20,22,24,30,25,31,23,33)(21,26,27,34,28,35,32,29)(36,37)(38,46)(39,49)(40,42)(41,44)(43,48)(45,51)(47,50);(36,38,40,45,41,48,39,47)(37,43,42,50,44,46,49,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2623);