Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
418 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,24,28,25,29,23,27)(22,30,32,26,33,34,31,35)(36,37,41,43,40,39,45,48)(38,44,46,51,47,42,49,50);(20,22)(21,26)(23,32)(24,31)(25,33)(27,34)(28,30)(29,35)(36,38,45,46,40,47,41,49)(37,42,43,51,39,44,48,50);(20,22)(21,26)(23,31)(24,32)(25,33)(27,30)(28,34)(29,35)(36,39)(37,40)(38,44)(41,43)(42,47)(45,48)(46,50)(49,51)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2363);