Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #157⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C33 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #157⋊D3 |
| commutator | C3×C3⋊D3 | C2×C4 |
| Fitting, socle | C2×C33 | D4 |
| prime radical, cosocle | C2×C3×C3⋊D3 | C22 |
| hypocenter | C33 | C4⋊C4 |
| LCS | G ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 13 points:
(1,2,3)(4,8,6,5)(7,9);(2,3)(7,8)(10,11,12,13)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=c,b^a=bc,e^a=f,f^a=e,g^a=g^2,e^b=f^2,f^b=e,e^c=e^2,f^c=f^230 conjugacy classes — view the full character table.
| maximal subgroup of | #11724102, #11724103, #11724105, … |
| maximal normal subgroup of | #11724102, #11724103, #11724105, … |
| maximal quotient of | #11722786, #11722787, #11722791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 587);