Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19716 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
678 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)(20,21,25,29)(22,30,32,27)(23,26,33,35)(24,34,31,28)(38,44)(39,46)(41,47)(43,49)(45,50)(48,51);(20,22,31,33,25,32,24,23)(21,26,34,27,29,35,28,30)(36,37)(38,41)(39,43)(40,42)(44,47)(45,48)(46,49)(50,51);(20,23,24,32,25,33,31,22)(21,27,28,26,29,30,34,35)(36,38,39,44,40,45,46,50)(37,41,43,47,42,48,49,51);(22,32)(23,33)(26,35)(27,30)(37,42)(41,48)(43,49)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12704);