Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#10471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(23,25,27,26)(28,29)(30,39)(31,44)(32,49)(33,37)(34,38)(35,41)(36,47)(40,55)(42,51)(43,54)(45,50)(46,53)(48,58)(52,57)(56,59);(21,24)(25,26)(28,30,34,43)(29,35,38,51)(31,45,47,56)(32,42,33,41)(36,52,44,55)(37,54,49,39)(40,46,57,48)(50,58,59,53);(21,25)(23,27)(24,26)(28,31,32,46,34,47,33,48)(29,36,37,53,38,44,49,58)(30,40,41,56,43,57,42,45)(35,50,39,52,51,59,54,55)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3459);