Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6312 |
| commutator, cosocle | C33×C4 | C22 |
| Frattini | C4 | C2×C3⋊(C3⋊D3) |
| Fitting | C33×D4 | C2 |
| socle | C2×C33 | D4 |
| hypercenter | D4 | C3⋊(C3⋊D3) |
| hypocenter | C33 | D8 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
308 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 4 generators on 17 points:
(2,5)(3,8)(6,7)(15,16,17);(1,2)(3,5)(4,7)(6,8)(10,11)(13,14)(16,17);(12,13,14);(9,10,11)Polycyclic presentation:
2^4,3^3|c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=g^2,c^b=cd72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3753, #11723544, C3⋊D3×#213, … |
| maximal normal subgroup of | D3×#3753, #11723544, C3⋊D3×#213, … |
| maximal quotient of | #11722177, #11722179, #11722196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 507);