Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24 |
| direct product | C2×C19×#1382 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | D8 |
| commutator | C8 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C23×C19 | #102 |
| prime radical | C24×C19 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(3,4,5,6)(7,8)(9,18)(10,23)(11,26)(12,28)(13,17)(14,19)(15,25)(16,24)(20,30)(21,38)(22,34)(27,31)(29,37)(32,36)(33,35);(7,9,11,20,24,35,25,36,13,22,10,19,12,21,27,37)(8,14,15,18,28,32,26,38,17,30,31,34,16,29,23,33)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5548);