Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
386 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)(20,21,26,31)(22,32,37,53)(23,38,42,75)(24,43,46,29)(25,47,50,74)(27,36,54,34)(28,55,58,41)(30,60,63,45)(33,66,39,76)(35,52,48,61)(40,78,44,62)(49,59,79,57)(51,80,56,71)(64,77,81,68)(65,70,82,72)(67,83,69,73);(20,22)(21,27)(23,39)(24,36)(25,48)(26,37)(28,56)(29,53)(30,61)(31,54)(32,43)(33,42)(34,46)(35,50)(38,73)(40,67)(41,68)(44,69)(45,70)(47,65)(49,71)(51,58)(52,63)(55,77)(57,81)(59,64)(60,72)(62,66)(74,82)(75,83)(76,78)(79,80);(20,23,26,42)(21,28,31,58)(22,33)(24,44,46,40)(25,49,50,79)(27,51)(29,59,43,57)(30,62,63,78)(32,64)(34,69)(35,71)(36,67)(37,39)(38,74,75,47)(41,60,55,45)(48,80)(52,66)(53,81)(54,56)(61,76)(65,83)(68,72)(70,77)(73,82)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6393);