Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11346 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C19 | C23 |
| commutator | C23 | C22×C8×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle, prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C19 ◁ G | |
878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 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)(22,23)(28,29)(30,35)(31,33)(32,34)(36,37,38,40,39,41,42,43);(21,23)(24,25)(26,27)(28,30,32,31)(29,33,34,35);(21,23)(25,27)(28,31,32,30)(29,33,34,35)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4334);