Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#7453 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1365 |
| commutator | C2×C16 | C2×C4×C19 |
| Frattini, cosocle | C4×C16 | C22×C19 |
| prime radical | C22×C19 | #361 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C4×C8×C19 ◁ C4×C16×C19 ◁ G | |
102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,30,25,43,22,34,24,42,35,46,36,51,37,29,27,33,41,28,45,32,39,50,26,31,40,49,44,47,38,48);(21,28,33,30)(22,35)(23,37)(24,26)(25,44)(29,32,48,43)(31,49,42,46)(34,47,50,51)(36,45)(38,41)(39,40)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 441);