Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88790 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C33 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6291 |
| commutator, Fitting, cosocle | C33×C4 | C22 |
| Frattini, hypercenter | C4 | D3×C3⋊D3 |
| socle, prime radical | C2×C33 | D4 |
| hypocenter | C33 | Q16 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,3,10,14,5,12,4,11)(2,6,13,16,8,15,7,9)(18,19)(21,22)(23,24,25);(1,2,5,8)(3,9,12,16)(4,13,10,7)(6,14,15,11)(20,21,22)(24,25);(17,18,19)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,g^a=g^2,e^b=e^2,f^b=f^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3719, #11722846, #11722855, … |
| maximal normal subgroup of | D3×#3719, #11722846, #11722855, … |
| maximal quotient of | #11722038, #11722041, #11722057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 446);