Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#10745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #120 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C25 | C23×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C25×C19 ◁ G | |
1794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(22,23)(28,29)(30,34,35,32)(31,33);(24,25,26,27)(28,30)(29,32)(31,35)(33,34);(21,23)(28,29)(30,32)(31,33)(34,35)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3733);