Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2801 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
420 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 420 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)(28,29,31,33)(30,34,35,32)(37,38)(41,42);(21,24)(25,27)(36,37,40,38)(39,42,43,41);(20,21,23,24)(22,25,26,27)(28,29)(30,32)(31,33)(34,35)(36,38,40,37)(39,42,43,41);(20,22,23,26)(21,25,24,27)(28,30,31,35)(29,32,33,34)(36,39,40,43)(37,41,38,42)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#36766, C19×#36769, C19×#36826, … |
| maximal normal subgroup of | C19×#36766, C19×#36769, C19×#36826, … |
| maximal quotient of | C19×#14434, C19×#14459, C19×#14504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1533);