Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| derived, Sylow | C33 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D33 |
| commutator, hypocenter | C33 | C22×C4 |
| Fitting, socle, cosocle | C2×C33 | C23 |
| prime radical | C2×#1113 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2 | |
270 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,3,4,2)(6,7)(8,9,10)(11,12,13);(1,2,4,3)(5,6,7)(9,10);(1,2,4,3)(12,13)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=d,c^2=d,g^a=g^2,f^b=f^2,e^c=e^254 conjugacy classes — view the full character table.
| maximal subgroup of | (D32⋊D3)⋊C4, #11724111, #11724118, … |
| maximal normal subgroup of | (D32⋊D3)⋊C4, #11724111, #11724118, … |
| maximal quotient of | #11722814, #11722820, #11722826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 596);