Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C2×C19×#1343 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | #99 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C19 |
| prime radical | C2×C19×#392 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C24×C19 ◁ C22×C22⋊C4×C19 ◁ G | |
1164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4)(5,13,15,8)(6,11)(7,12)(9,14,17,18)(10,16);(4,8)(5,14)(9,11)(10,17)(12,13)(15,18)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4677);