Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of (C2×D3)⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | (C2×D3)⋊#157 |
| Sylow | C33 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#157 |
| commutator, Fitting, socle | C2×C33 | C2×C4 |
| prime radical | C2×D3×C3⋊D3 | C2 |
| cosocle | C2×C3×C3⋊D3 | C22 |
| hypocenter | C33 | C22⋊C4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 | |
152 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 13 points:
(2,4)(5,6,7)(8,9)(10,11,13,12);(1,2)(3,4)(6,7)(8,10,13)Polycyclic presentation:
2^4,3^3|b^2=c,b^a=bd,g^a=g^2,e^b=e^2f,f^b=ef,e^c=e^2,f^c=f^230 conjugacy classes — view the full character table.
| maximal subgroup of | #11724112, #11724113, #11724121, … |
| maximal normal subgroup of | #11724112, #11724113, #11724121, … |
| maximal quotient of | #11722706, #11722707, #11722708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 568);