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) = C24 |
| direct product | C19×#13190 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C19 | C23 |
| commutator | C23 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C23×C19 | C22×C8 |
| prime radical | C22×D4×C19 | C8 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C19 ◁ G | |
522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
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)(21,23)(25,27)(28,29,33,37,34,36,41,42,32,30,35,39,31,38,40,43);(20,21,22,23)(28,30,33,39,34,38,41,43,32,29,35,37,31,36,40,42);(24,25,26,27)(28,31,32,34)(29,36,30,38)(33,40,35,41)(37,42,39,43)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6178);