Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1366 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#11956 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #333 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| socle | C2×C19 | C2×#333 |
| prime radical | C23×C19 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
292 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)(20,21,24,28,37,29,47,45,25,30,39,46,23,27,36,43)(22,31,34,44,32,42,38,50,33,48,49,51,35,26,40,41);(20,22,25,33)(21,26)(23,32,37,35)(24,38,39,40)(27,31)(28,44)(29,48)(30,42)(34,36,49,47)(41,45)(43,50)(46,51);(20,23,25,37)(21,27,30,29)(22,32,33,35)(24,36,39,47)(26,31,42,48)(28,43,46,45)(34,38,49,40)(41,44,50,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4944);