Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17367 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17372 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×Q8×C19 ◁ G | |
1174 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,25,23,24,26,27)(28,29,33,39,34,38,32,37)(30,36,40,43,31,35,41,42);(28,30,34,31)(29,35,38,36)(32,40,33,41)(37,42,39,43);(21,24)(25,27)(28,31,34,30)(29,36,38,35)(32,40,33,41)(37,42,39,43);(28,32,34,33)(29,37,38,39)(30,40,31,41)(35,42,36,43)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10360);