Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21846 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C22×C22⋊C4 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C19×#117 ◁ G | |
938 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37,40,44,41,39,48,43)(38,42,47,50,46,45,51,49);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38)(37,42)(39,45)(40,47)(41,46)(43,49)(44,50)(48,51);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,39)(37,41)(38,45)(40,43)(42,46)(44,48)(47,49)(50,51);(21,27)(25,28)(26,35)(33,34)(38,46)(42,45)(47,51)(49,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14834);