Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C33 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #1113 |
| commutator, hypocenter | C33 | C2×C8 |
| Fitting, cosocle | C33×C4 | C22 |
| socle | C2×C33 | C2×C4 |
| prime radical | C2×C3×C3⋊D3 | C4 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
126 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,5,4,6,7,8)(9,10)(13,14)(15,16,17);(10,11)(12,13,14)(16,17)Polycyclic presentation:
2^4,3^3|b^2=c,c^2=d,e^a=e^2,g^a=g^2,e^b=e^2,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | D32⋊(C3⋊C8), #11722758, #11722760, … |
| maximal normal subgroup of | D32⋊(C3⋊C8), #11722758, #11722760, … |
| maximal quotient of | #11722065, #11722066, #11722070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 455);