Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88851 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C33×C8 ⋊ C2 |
| Sylow | C33 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊(C3⋊(C3⋊D3)) |
| commutator, cosocle | C33×C4 | C22 |
| Frattini | C4 | C2×C3⋊(C3⋊D3) |
| Fitting | C33×C8 | C2 |
| socle | C2×C33 | D4 |
| hypercenter | C8 | C3⋊(C3⋊D3) |
| hypocenter | C33 | D8 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
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:
(1,2,6,8,4,7,3,5)(15,16,17);(2,5)(3,6)(7,8)(10,11)(13,14)(16,17);(12,13,14);(9,10,11)Polycyclic presentation:
2^4,3^3|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=g^2111 conjugacy classes — view the full character table.
| maximal subgroup of | #11722005, #11722006, #11722010, … |
| maximal normal subgroup of | #11722005, #11722006, #11722010, … |
| maximal quotient of | #11722169, #11722170, #11722171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 499);