Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#12658 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C42 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C2×#97 |
| prime radical | C23×C19 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ G | |
350 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)(20,21,22,23)(25,30,32,38)(26,34)(28,37)(31,39,33,35);(21,23)(24,25,28,33,27,30,34,39,29,32,37,31,36,38,26,35);(24,26,27,28,29,34,36,37)(25,31,38,39,32,33,30,35)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5646);