Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#18408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3497 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
1170 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)(22,26)(23,25)(24,27)(28,29,33,31)(30,36,38,43)(32,40,42,35)(34,41,37,39);(21,25)(22,23)(26,27)(28,30)(29,34)(31,37)(32,41)(33,38)(35,43)(36,40)(39,42);(28,31,33,29)(30,37,38,34)(32,35,42,40)(36,41,43,39);(20,22,24,23)(21,25,27,26)(30,38)(34,37)(36,43)(39,41)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11396);