Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2646 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C24×C19 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
436 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,25)(22,23,26,27)(29,30)(33,34)(36,37)(38,41)(39,42)(40,43);(21,25)(22,26)(28,29,32,30)(31,33,35,34)(36,38)(37,40)(39,43)(41,42);(20,22)(21,23)(24,26)(25,27)(28,30,32,29)(31,33,35,34)(36,38)(37,41)(39,43)(40,42);(20,23)(21,26)(22,25)(24,27)(28,31)(29,33)(30,34)(32,35)(36,37)(38,40)(39,42)(41,43)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10344, C19×#10345, C19×#10346, … |
| maximal normal subgroup of | C19×#10344, C19×#10345, C19×#10346, … |
| maximal quotient of | C19×#14265, C19×#14275, C19×#14329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1378);