Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19027 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3561 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
884 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)(20,21,24,27)(22,28,29,35)(23,31,33,26)(25,32,34,30)(38,44)(39,46)(41,49)(42,47)(45,48)(50,51);(20,22,24,29)(21,25,27,34)(23,32,33,30)(26,35,31,28)(36,37,40,43)(38,41,45,50)(39,47,46,42)(44,51,48,49);(23,33)(26,31)(28,35)(30,32)(36,38)(37,41)(39,48)(40,45)(42,51)(43,50)(44,46)(47,49);(22,29)(25,34)(28,35)(30,32)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12015);