Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | H(3,𝔽3) ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3×C8 | C3⋊D3 |
| commutator, hypocenter | H(3,𝔽3) | C16 |
| Fitting, cosocle | C8×H(3,𝔽3) | C2 |
| socle | C2×C3 | C3⋊(C3⋊C8) |
| prime radical | C2×H(3,𝔽3) | C8 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C3×C8 | |
55 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 25 points:
(2,4)(5,9)(6,8)(10,11,12,15,13,16,18,21,14,17,19,22,20,23,24,25);(2,5,6)(4,8,9);(1,2,4)(3,6,8)(5,9,7)Polycyclic presentation:
2^4,3^3|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^2,f^e=fg80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 33);