Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13627 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C19 | C23 |
| commutator | C22 | C22×C16×C19 |
| Frattini, cosocle | C2×C16 | C23×C19 |
| socle | C22×C19 | C22×C16 |
| prime radical | C23×C19 | C2×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C19 ◁ G | |
218 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,26,31,27,32,34,43,28,33,35,44,37,45,46,53,29,30,36,40,38,41,47,50,39,42,48,51,49,52,54,55);(20,21,22,23);(25,30)(31,40)(32,41)(33,42)(43,50)(44,51)(45,52)(53,55)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6615);