Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×#627 |
| Sylow | C33 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D33 |
| commutator, Fitting, socle, cosocle | C2×C33 | C23 |
| prime radical | C2×C32×D3 | C22 |
| hypocenter | C33 | C2×Q8 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 | |
198 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,3,4,8)(2,5,6,7)(9,10,11)(13,14)(15,16,17);(1,2,4,6)(3,7,8,5)(12,13,14)(16,17);(10,11)45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3775, D3×#3776, #11724142, … |
| maximal normal subgroup of | D3×#3775, D3×#3776, #11724142, … |
| maximal quotient of | D3×Dic3⋊Dic3, D3×#3724, Dic3×#627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 603);