Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7469 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C19 | C22⋊C4 |
| commutator | C22 | C4×C16×C19 |
| Frattini, cosocle | C22×C16 | C22×C19 |
| socle | C2×C19 | #1374 |
| prime radical | C23×C19 | C2×C16 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C19 ◁ C22×C16×C19 ◁ G | |
174 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)(20,21,23,28,24,30,37,48,25,31,38,49,40,52,61,72,26,29,39,47,41,50,62,70,42,51,63,71,64,73,79,82)(22,32,34,53,35,54,58,74,36,55,59,75,60,76,78,83,33,27,43,44,56,45,65,67,57,46,66,68,77,69,80,81);(20,22)(21,27,29,32)(23,34)(24,35)(25,36)(26,33)(28,44,47,53)(30,45,50,54)(31,46,51,55)(37,58)(38,59)(39,43)(40,60)(41,56)(42,57)(48,67,70,74)(49,68,71,75)(52,69,73,76)(61,78)(62,65)(63,66)(64,77)(72,81,82,83)(79,80)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 457);