Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33619 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#466 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,27,33)(22,34,37,60)(23,41,44,58)(24,45,47,56)(25,32,26,31)(28,49,51,38)(29,48,55,43)(30,46,57,35)(36,65,66,82)(39,62,40,61)(42,73,74,54)(50,77,78,83)(52,69,53,63)(59,70,81,68)(64,72,75,80)(67,71,76,79);(20,22,35,63,26,40,47,49,27,37,46,69,25,39,24,38)(21,28,45,62,32,53,57,60,33,51,56,61,31,52,30,34)(23,36,64,83,43,68,74,76,44,66,75,77,48,70,42,67)(29,50,72,65,41,71,73,81,55,78,80,82,58,79,54,59);(20,23)(21,29)(22,36)(24,42)(25,48)(26,43)(27,44)(28,50)(30,54)(31,58)(32,41)(33,55)(34,59)(35,64)(37,66)(38,67)(39,70)(40,68)(45,72)(46,75)(47,74)(49,76)(51,78)(52,79)(53,71)(56,80)(57,73)(60,81)(61,82)(62,65)(63,83)(69,77);(22,37)(28,51)(34,60)(36,66)(38,49)(39,40)(50,78)(52,53)(59,81)(61,62)(63,69)(65,82)(67,76)(68,70)(71,79)(77,83)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26607);