Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#2760 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C19×#392 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
520 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 520 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) = 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)(21,24)(22,26)(28,29,32,30)(31,34,35,33)(36,37)(38,42)(39,40)(41,43);(21,24)(25,27)(29,30)(31,35)(37,40)(38,43);(20,21,23,24)(22,25,26,27)(28,30,32,29)(31,34,35,33)(36,38)(37,41)(39,43)(40,42);(20,22)(21,25)(23,26)(24,27)(28,31)(29,33)(30,34)(32,35)(36,37)(38,41)(39,40)(42,43)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12187, C19×#12263, C19×#36776, … |
| maximal normal subgroup of | C19×#12187, C19×#12263, C19×#36776, … |
| maximal quotient of | C19×#14375, C19×#14508, C19×#14572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1492);