Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23888 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,29,26)(27,34,36,39)(28,30,38,32)(31,37,33,35);(25,30)(26,32)(28,38)(31,34)(33,39)(35,37);(21,23)(24,26)(25,29)(27,33)(28,30)(31,36)(32,38)(34,37)(35,39);(24,27)(25,31)(26,33)(28,37)(29,36)(30,34)(32,39)(35,38)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16876);