Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32698 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,28,24,29,33,35)(22,26,27,34,30,23,31,32);(20,22)(21,26)(23,29)(24,30)(25,31)(27,33)(28,32)(34,35);(20,23)(21,27,29,31)(22,28,30,35)(24,26)(25,32)(33,34);(22,30)(25,33)(28,35)(32,34)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25686);