Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10145 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C2×C19×#493 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29)(30,33)(31,35)(32,34);(22,26)(24,27)(29,33)(30,32)(34,35);(20,21)(22,27)(23,25)(24,26)(28,29,31,35)(30,33,32,34)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3133);