Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7262 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7278 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #340 |
| commutator | C2×C8 | C42×C19 |
| Frattini, cosocle | C2×C4×C8 | C22×C19 |
| prime radical | C23×C19 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 2 generators on 43 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)(25,27)(29,34,35,38)(30,31)(32,40)(36,43,42,37)(39,41);(21,24)(22,27)(25,26)(28,29,31,36,40,43,30,38,33,35,41,42,32,37,39,34)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 266);