Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88810 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C33 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6295 |
| commutator, Fitting, cosocle | C33×C4 | C22 |
| Frattini, hypercenter | C4 | #1113 |
| socle, prime radical | C2×C33 | D4 |
| hypocenter | C33 | Q16 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(17,18)(21,22)(23,24,25);(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10)(18,19)(20,21,22)(24,25)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,g^a=g^2,c^b=cd,e^b=e^2,f^b=f^245 conjugacy classes — view the full character table.
| maximal subgroup of | #11722767, #11722768, #11722789, … |
| maximal normal subgroup of | #11722767, #11722768, #11722789, … |
| maximal quotient of | #11722076, #11722080, C2×#88812, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 459);