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×#13645 |
| 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 | C2×D4×C19 | C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C19 ◁ G | |
204 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)(20,21)(22,23)(24,25,27,32,28,33,39,47,29,26,35,36,41,37,50,51,30,34,40,48,42,49,53,55,43,38,31,44,45,52,46,54);(21,23);(24,26,27,36,28,37,39,51,29,34,35,48,41,49,50,55,30,38,40,44,42,52,53,54,43,25,31,32,45,33,46,47)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6633);