Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#7464 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #367 |
| commutator | C16 | C2×C8×C19 |
| Frattini, cosocle | C4×C16 | C22×C19 |
| socle | C2×C19 | #1372 |
| prime radical | C22×C19 | #368 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×C8×C19 ◁ C4×C8×C19 ◁ C4×C16×C19 ◁ G | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 2 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,26,31,47,57,27,33,42,61,49,32,25,48)(22,34,37,63,39,65,38,75,40,67,46,64,76,66,77,83)(23,41,35,58,44,78,68,60,45,79,69,59,74,51,43,29)(28,50,52,81,54,82,80,36,56,70,53,72,55,71,62,73);(20,22,35,50,25,38,23,36,49,76,43,71,42,37,74,81,27,40,69,70,47,77,45,73,26,39,68,82,24,46,44,72)(21,28,51,75,30,53,29,34,31,54,41,64,57,62,58,65,33,56,78,83,61,52,60,67,32,55,79,63,48,80,59,66)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 452);