Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12506 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C8 |
| direct product | C19×#12514 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | #493 |
| commutator, Frattini, cosocle | C4×C8 | C23×C19 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C82×C19 ◁ G | |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,31)(24,26)(25,29)(27,32)(30,34)(33,35)(36,37,44,51)(38,52,57,46)(39,58,53,45)(40,48,59,67)(41,47,61,65)(42,50,43,49)(54,64,60,63)(55,66,56,62);(20,22,23,29,24,30,32,35)(21,25,27,28,26,33,31,34)(36,38,41,54,42,55,59,39,44,57,61,60,43,56,40,53)(37,45,48,62,49,63,65,46,51,58,67,66,50,64,47,52);(21,26)(25,33)(27,31)(28,34)(36,39,59,56,43,54,41,57,44,53,40,55,42,60,61,38)(37,46,65,64,50,62,48,58,51,52,47,63,49,66,67,45)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5502);