Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | D4×C3⋊D9 |
| Fitting | C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×C3⋊D9 |
| commutator, cosocle | C2×C3×C9 | C23 |
| Frattini | C2×C3 | C22×C3⋊D3 |
| Fitting | C3×D4×C9 | C2 |
| socle | C2×C32 | C22×D3 |
| hypercenter | D4 | C3⋊D9 |
| hypocenter | C3×C9 | C2×D4 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ D4 | |
270 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3)(5,7)(6,10)(8,9)(11,12);(1,2,3)(14,16);(4,9,11,10,5,7,6,12,8)(13,14)(15,16)75 conjugacy classes — view the full character table.
| maximal subgroup of | #11721174, #11721179, #11721182, … |
| maximal normal subgroup of | #11721174, #11721179, #11721182, … |
| maximal quotient of | #11721724, C22⋊C4×C3⋊D9, #11721727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 388);