Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7333 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#7333 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #322 |
| commutator | C8 | C4×C8×C19 |
| Frattini, cosocle | #346 | C22×C19 |
| socle | C2×C19 | #1313 |
| prime radical | C22×C19 | #347 |
| LCS | G ▷ C8 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C19×#346 ◁ G | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,27,23,29,33,43,24,28,34,45,36,40,50,51,25,30,32,44,35,47,49,41,37,46,31,42,48,26,38,39);(21,26,28,29,30,40,46,47)(22,31,32,34)(23,35)(27,41,42,51,44,43,45,39)(33,50,49,38)(36,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 321);