Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#7332 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C42 |
| commutator | C4 | C4×C16×C19 |
| Frattini, cosocle | C4×C16 | C22×C19 |
| socle, prime radical | C22×C19 | #346 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ G | |
106 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)(20,21,22,25,23,24,26,27)(28,29,31,38,33,39,34,32,36,41,51,52,35,40,50,53)(30,42,43,58,45,56,59,57,48,55,49,44,47,37,46,54);(21,24)(25,27)(28,30,32,44,34,46,40,55,35,47,38,57,31,49,41,56,36,48,53,58,50,59,39,42,33,45,52,54,51,43,29,37)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 320);