Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1462 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#1799 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C19 |
| Frattini, cosocle | C24 | C23×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
380 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 124 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) = 608 |
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)(21,23)(24,25)(26,30,31,28)(27,29);(20,21,22,23);(24,26)(25,28)(27,31)(29,30)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7236, C19×#7237, C19×#7320, … |
| maximal normal subgroup of | C19×#7236, C19×#7237, C19×#7320, … |
| maximal quotient of | C19×#8557, C19×#8558, C19×#8559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 531);