Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6189 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3×C9 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×D9 |
| commutator | C2×C3×C9 | C2×C4 |
| Frattini | C3×C4 | D32 |
| Fitting, cosocle | C3×C4×C9 | C22 |
| socle | C2×C32 | C2×Dic3 |
| prime radical | C2×C3×D3 | Dic3 |
| hypocenter | C3×C9 | M16 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C4 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3)(5,7)(6,10)(8,9)(11,12)(13,14,15,18,16,17,19,20);(2,3)(4,9,11,10,5,7,6,12,8)(14,17)(18,20)Polycyclic presentation:
2^4,3^3|b^2=c,c^2=d,e^3=g^2,b^a=bd,f^a=f^2,e^b=e^2g,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | D9×ΓL(1,𝔽25), #11720801, #11720806, … |
| maximal normal subgroup of | D9×ΓL(1,𝔽25), #11720801, #11720806, … |
| maximal quotient of | #11720258, Dic3⋊(C9⋊C8), (C2×D3)⋊(C9⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 67);