Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33570 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C19 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
1212 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)(22,28)(23,26)(24,27)(25,30)(29,33)(31,35)(32,34);(21,26)(22,23)(24,33)(27,34)(28,30)(29,35);(21,27)(24,33)(26,34)(28,35)(29,30)(31,32);(20,22,25,23)(21,28,30,26)(24,31,33,32)(27,35,29,34)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26558);