Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13334 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13335 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2011 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3414 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 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)(22,32)(23,37)(24,42)(25,48)(26,30)(27,34)(28,39)(29,46)(31,45)(33,51)(35,73)(36,65)(38,56)(40,78)(41,55)(43,61)(44,62)(47,63)(49,58)(50,59)(52,72)(53,79)(54,69)(57,77)(60,70)(64,67)(66,75)(68,83)(71,81)(74,82)(76,80);(20,22,26,36)(21,27,30,52)(23,33,41,69)(24,43,47,79)(25,49,45,35)(28,54,56,51)(29,58,60,73)(31,61,48,53)(32,63,65,42)(34,70,72,46)(37,75,55,64)(38,76,39,71)(40,74,50,68)(44,67,77,66)(57,82,62,83)(59,80,78,81);(20,23)(21,28)(22,33)(24,44)(25,50)(26,41)(27,51)(29,59)(30,56)(31,62)(32,64)(34,71)(35,74)(36,69)(37,42)(38,70)(39,46)(40,45)(43,67)(47,77)(48,57)(49,68)(52,54)(53,83)(55,63)(58,81)(60,78)(61,82)(65,75)(66,79)(72,76)(73,80)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6323);