Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88790 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C33 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6291 |
| commutator, Fitting, cosocle | C33×C4 | C22 |
| Frattini, hypercenter | C4 | D3×C3⋊D3 |
| socle | C2×C33 | D4 |
| hypocenter | C33 | D8 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ 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:
(1,2,6,8,4,7,3,5)(10,11)(13,14)(15,16,17);(2,5)(3,6)(7,8)(12,13,14)(16,17);(9,10,11)Polycyclic presentation:
2^4,3^3|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×#3714, #11722830, #11722853, … |
| maximal normal subgroup of | D3×#3714, #11722830, #11722853, … |
| maximal quotient of | #11722005, #11722009, #11722010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 437);