Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88810 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C33 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6295 |
| commutator, Fitting, cosocle | C33×C4 | C22 |
| Frattini, hypercenter | C4 | #1113 |
| socle | C2×C33 | D4 |
| hypocenter | C33 | D8 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(2,5)(3,8)(6,7)(9,10)(13,14)(15,16,17);(1,2)(3,5)(4,7)(6,8)(10,11)(12,13,14)(16,17)Polycyclic presentation:
2^4,3^3|c^2=d,b^a=bc,c^a=cd,e^a=e^2,g^a=g^2,c^b=cd,e^b=e^2,f^b=f^245 conjugacy classes — view the full character table.
| maximal subgroup of | #11722765, #11722766, #11722788, … |
| maximal normal subgroup of | #11722765, #11722766, #11722788, … |
| maximal quotient of | #11722067, #11722068, #11722069, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 457);