Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19254 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19277 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
638 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,24,27)(22,28,31,35)(23,32,29,26)(25,33,34,30)(36,37)(38,46)(39,45)(40,42)(41,44)(43,47)(48,51)(49,50);(20,22,29,33,24,31,23,30)(21,25,32,35,27,34,26,28)(37,42)(43,50)(44,45)(46,51);(36,38)(37,43)(39,47)(40,48)(41,49)(42,50)(44,46)(45,51);(36,39,40,41)(37,44,42,45)(38,47,48,49)(43,46,50,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12265);