Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9303 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9312 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,24,23,26,27,25)(28,29)(30,39,42,50)(31,43)(32,37)(33,47)(34,38)(35,41,51,46)(36,44)(40,55,58,49)(45,52)(48,53)(54,56,59,57);(21,24,26,25)(28,30,32,46,34,42,33,41)(29,35,37,50,38,51,47,39)(31,40,44,57,45,58,48,56)(36,49,52,59,53,55,43,54);(28,31)(29,36)(30,40)(32,44)(33,48)(34,45)(35,49)(37,52)(38,53)(39,54)(41,56)(42,58)(43,47)(46,57)(50,59)(51,55)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2300);