Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33340 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | C22×D4 |
| commutator | C4 | C23×C8×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C22×C22⋊C8 |
| prime radical | C19×#585 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C2×C19×#131 ◁ G | |
1114 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)(20,21,25,31,26,32,46,59,27,33,47,60,24,30,44,57)(22,34,37,62,36,51,66,58,38,56,45,72,43,28,48,50)(23,29,41,54,42,55,71,80,39,52,67,76,40,53,69,78)(35,61,65,81,64,74,82,79,63,77,70,83,68,49,73,75);(20,22)(21,28)(23,35)(24,43)(25,45)(26,36)(27,38)(29,49)(30,56)(31,58)(32,34)(33,51)(37,47)(39,63)(40,68)(41,70)(42,64)(44,66)(46,48)(50,60)(52,74)(53,77)(54,79)(55,61)(57,62)(59,72)(65,67)(69,82)(71,73)(75,76)(78,81)(80,83);(20,23)(21,29)(22,35)(24,40)(25,41)(26,42)(27,39)(28,49)(30,53)(31,54)(32,55)(33,52)(34,61)(36,64)(37,65)(38,63)(43,68)(44,69)(45,70)(46,71)(47,67)(48,73)(50,75)(51,74)(56,77)(57,78)(58,79)(59,80)(60,76)(62,81)(66,82)(72,83);(23,39)(29,52)(35,63)(40,42)(41,67)(49,74)(53,55)(54,76)(61,77)(64,68)(65,70)(69,71)(73,82)(75,79)(78,80)(81,83)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26328);