Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2127 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#2128 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×#99 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×D4 | C23×C19 |
| prime radical | C19×#535 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
270 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,27,31,25)(24,28)(29,34)(30,33,35,32);(21,25)(22,29)(23,31)(26,33)(27,28)(32,34);(20,22,24,29)(21,26,28,34)(23,30,31,35)(25,32,27,33)437 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12711, C19×#12714, C19×#12722, … |
| maximal normal subgroup of | C19×#12711, C19×#12714, C19×#12722, … |
| maximal quotient of | C19×#11433, C19×#11450, C19×#11480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 860);