Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#1898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C19 |
| Frattini, cosocle | C24 | C23×C19 |
| prime radical | C2×C19×#120 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C25×C19 ◁ G | |
598 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 304 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25)(26,28,30,31)(27,29);(24,26)(25,28,29,31)(27,30);(21,23)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#8534, C19×#8535, C2×C19×#1898, … |
| maximal normal subgroup of | C19×#8534, C19×#8535, C2×C19×#1898, … |
| maximal quotient of | C19×#9079, C19×#9081, C19×#9083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 630);