Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13402 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#13403 |
| 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 | |
384 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)(22,32,37,52)(23,38,43,73)(24,44,46,29)(25,47,49,71)(27,36,53,34)(28,54,58,41)(30,59,61,45)(33,63,66,83)(35,51,70,81)(39,74,64,82)(40,72,42,60)(48,57,75,56)(50,78,80,68)(55,77,79,65)(62,67,76,69);(20,22)(21,27)(23,39)(24,36)(25,35)(26,37)(28,55)(29,52)(30,51)(31,53)(32,44)(33,42)(34,46)(38,63)(40,66)(41,68)(43,64)(45,69)(47,76)(48,77)(49,70)(50,57)(54,78)(56,80)(58,79)(59,67)(60,82)(61,81)(62,71)(65,75)(72,74)(73,83);(20,23,26,43)(21,28,31,58)(22,33)(24,42,46,40)(25,48,49,75)(27,50)(29,57,44,56)(30,60,61,72)(32,55)(34,39)(35,68)(36,64)(37,66)(38,71,73,47)(41,59,54,45)(51,63)(52,79)(53,80)(62,82)(65,69)(67,77)(70,78)(74,76)(81,83)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6391);