Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D3×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived, Sylow | C33 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×C3⋊D3 |
| commutator, hypocenter | C33 | C2×C8 |
| Fitting, cosocle | C33×C4 | C22 |
| socle | C2×C33 | C2×C4 |
| prime radical | C2×C3⋊(C3⋊D3) | C4 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,3,4,8,5,2,6,7)(10,11)(13,14)(15,16,17);(1,2,4,7,5,3,6,8)(12,13,14)(16,17);(9,10,11)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=c,c^2=d,g^a=g^2,e^b=e^2,f^b=f^272 conjugacy classes — view the full character table.
| maximal subgroup of | #11722719, #11722721, D3×#3710, … |
| maximal normal subgroup of | #11722719, #11722721, D3×#3710, … |
| maximal quotient of | #11722000, #11722003, #11722018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 432);