Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88543 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6233 |
| commutator, cosocle | C3×C4×C9 | C22 |
| Frattini | C3×C4 | C2×C3⋊D3 |
| Fitting | C3×D4×C9 | C2 |
| socle | C2×C32 | #67 |
| hypercenter | D4 | C3⋊D9 |
| hypocenter | C3×C9 | D8 |
| LCS | G ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3)(14,17)(15,20)(18,19);(2,3)(5,7)(6,10)(8,9)(11,12)(13,14)(15,17)(16,19)(18,20);(4,5,8,10,12,11,6,9,7)Polycyclic presentation:
2^4,3^3|c^2=d,e^3=g^2,b^a=bc,c^a=cd,e^a=e^2g,f^a=f^2,g^a=g^2,c^b=cd72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3673, #11721167, #11721170, … |
| maximal normal subgroup of | D3×#3673, #11721167, #11721170, … |
| maximal quotient of | #11720525, #11720528, #11720563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 191);