Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #13694 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C19 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C4×C8×C19 ◁ C4×C16×C19 ◁ G | |
270 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)(25,30)(26,31)(27,35)(28,38)(32,47)(33,50)(34,43)(36,52)(37,46)(39,51)(40,41)(42,48)(44,45)(49,55)(53,54);(24,25,31,41,27,32,44,50,38,48,52,55,51,53,37,43,29,34,46,54,39,49,36,42,28,33,45,47,35,40,26,30);(20,21,22,23)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6713);