Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C25 |
| direct product | C2×C19×#1390 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #99 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C22×D4 | C23×C19 |
| prime radical | C23×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C19 ◁ C23×D4×C19 ◁ G | |
1202 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(7,8)(9,13,14,11)(10,12);(3,4,5,6)(8,11)(12,13)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5560);