Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88810 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C33 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6295 |
| commutator, Fitting, cosocle | C33×C4 | C22 |
| Frattini, hypercenter | C4 | #1113 |
| socle | C2×C33 | D4 |
| prime radical | C3×C4⋊(C3⋊D3) | C2 |
| hypocenter | C33 | SD16 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
122 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4,6)(3,8,7,5)(9,10)(13,14)(15,16,17);(2,5)(3,7)(6,8)(10,11)(12,13,14)(16,17)Polycyclic presentation:
2^4,3^3|b^2=d,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 | D3×#3715, D3×#3716, D3×#3717, … |
| maximal normal subgroup of | D3×#3715, D3×#3716, D3×#3717, … |
| maximal quotient of | #11722075, #11722076, #11722079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 458);