Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C82×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#7330 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C42 |
| commutator | C4 | C82×C19 |
| Frattini, cosocle | C4×C16 | C22×C19 |
| socle, prime radical | C22×C19 | #346 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 2 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(28,29,30,35,31,37,40,50,32,38,41,48,42,52,54,58,33,36,39,49,43,51,53,59,44,34,45,46,55,47,56,57);(20,21,22,24,23,25,26,27)(29,34,36,38)(30,39)(35,48,49,46)(37,47,51,52)(40,53)(41,45)(50,58,59,57)(54,56)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 318);