Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13163 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C2×D4 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×C4⋊C8 |
| prime radical | C23×C19 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ C2×C4×C8×C19 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,28,26,27,31,36,34,29,32,38,35,37,30,39,33);(24,26,28,31,27,34,36,32,29,35,38,30,37,33,39,25);(20,21,22,23)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6151);