Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#3417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C24×C19 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ #41×C19 ◁ C19×#131 ◁ G | |
350 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(20,21,26,31)(22,32,36,60)(23,28,37,51)(24,40,44,58)(25,45,42,30)(27,47,50,34)(29,54,56,43)(33,59,61,81)(35,64,46,55)(38,67,65,80)(39,70,66,53)(41,57,72,49)(48,73,74,62)(52,77,76,69)(63,82,71,78)(68,79,83,75);(20,22,26,36)(21,27,31,50)(23,33,37,61)(24,41,44,72)(25,46,42,35)(28,48,51,74)(29,55,56,64)(30,57,45,49)(32,58,60,40)(34,54,47,43)(38,68,65,83)(39,71,66,63)(52,78,76,82)(53,79,70,75)(59,80,81,67)(62,77,73,69);(20,23)(21,28)(22,33)(24,38)(25,39)(26,37)(27,48)(29,52)(30,53)(31,51)(32,59)(34,62)(35,63)(36,61)(40,67)(41,68)(42,66)(43,69)(44,65)(45,70)(46,71)(47,73)(49,75)(50,74)(54,77)(55,78)(56,76)(57,79)(58,80)(60,81)(64,82)(72,83);(23,37)(28,51)(33,61)(38,65)(39,66)(48,74)(52,76)(53,70)(59,81)(62,73)(63,71)(67,80)(68,83)(69,77)(75,79)(78,82)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#13670, C19×#13672, C19×#33855, … |
| maximal normal subgroup of | C19×#13670, C19×#13672, C19×#33855, … |
| maximal quotient of | C19×#33382, C19×#33410, C19×#33455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 2149);