Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#2537 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
788 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(25,27);(20,21,23,22)(28,29,30,31);(24,25)(26,27)(28,29)(30,31);(20,22,23,21)722 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10228, C19×#10231, C19×#10235, … |
| maximal normal subgroup of | C19×#10228, C19×#10231, C19×#10235, … |
| maximal quotient of | C19×#13906, C19×#13970, C19×#13994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1269);