Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C19×#1930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
1026 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(3,4,6,5)(8,12)(9,15)(10,17)(13,20)(14,19)(18,21);(3,5,6,4)(7,8,10,12,11,14,17,19)(9,13,16,18,15,21,22,20);(7,9,10,16,11,15,17,22)(8,13,12,18,14,21,19,20)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14061);