Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#2736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C25×C19 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 608 |
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)(22,26)(23,24)(25,27)(28,29,32,33)(30,34,35,31)(36,37,39,41)(38,42,43,40);(21,24)(22,27)(29,33)(31,34)(36,37,39,41)(38,40,43,42);(20,22)(21,25)(23,27)(24,26)(28,30)(29,31)(32,35)(33,34)(36,37)(38,40)(39,41)(42,43);(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,34)(33,35)(36,38)(37,40)(39,43)(41,42)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12188, C19×#12264, C19×#36725, … |
| maximal normal subgroup of | C19×#12188, C19×#12264, C19×#36725, … |
| maximal quotient of | C19×#14366, C19×#14481, C19×#14577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1468);