Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C33 |
No aliases for this group.
| Sylow | C33 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×C3⋊(C3⋊D3) |
| commutator | C2×C33 | C2×C4 |
| Fitting, prime radical | C23×C33 | C2 |
| socle, cosocle | C22×C33 | C22 |
| hypercenter | C23 | C3⋊(C3⋊D3) |
| hypocenter | C33 | C22⋊C4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C22 ◁ C23 | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 4 generators on 17 points:
(6,8)(15,16,17);(1,2,3,4)(5,6)(7,8)(10,11)(13,14)(16,17);(12,13,14);(9,10,11)Polycyclic presentation:
2^4,3^3|a^2=c,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #11722062, #11722063, #11722176, … |
| maximal normal subgroup of | #11722062, #11722063, #11722176, … |
| maximal quotient of | #11722200, #11722201, #11722202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 511);