Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9159 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C22×D4×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
494 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)(20,21,24,27,25,29,23,28)(22,30,32,34,33,35,31,26)(36,37)(38,46,39,42)(40,45)(41,44)(43,48,50,47)(49,51);(20,22)(21,26,29,34)(23,31)(24,32)(25,33)(27,30,28,35)(36,38,40,39)(37,42)(41,48,49,47)(43,44)(45,46)(50,51);(21,27)(23,24)(26,30)(28,29)(31,32)(34,35)(36,39,40,38)(37,43,45,50)(41,47,49,48)(42,44,46,51)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2165);