Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1404 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#1405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C2×C4×C19 |
| Frattini, cosocle | C4⋊Q8 | C22×C19 |
| prime radical | C19×2−1+4 | C4 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C19 ◁ C2×C4×C19 ◁ C19×C4⋊Q8 ◁ G | |
106 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 28 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 — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,27,25,22,29,31)(24,28,34,26,35,32,33,30);(20,22)(21,25)(23,26)(24,28)(27,34)(29,30)(31,33)(32,35)323 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×#1405, C19×#13572, C19×#13573, … |
| maximal normal subgroup of | C2×C19×#1405, C19×#13572, C19×#13573, … |
| maximal quotient of | C19×#7345, C19×#7376, C19×#7409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 137);