Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88989 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C33 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C3⋊#157 |
| commutator, socle | C2×C33 | C2×C4 |
| Fitting | C33×C4 | C4 |
| prime radical | C2×C3×C3⋊D3 | C4 |
| cosocle | C3×C3⋊Dic3 | C22 |
| hypercenter | C4 | C3⋊#157 |
| hypocenter | C33 | M16 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,3,5,4)(2,6,7,8)(9,10,11)(12,14,17);(1,2,4,6,5,7,3,8)(10,11)(12,13)(14,15,17,16)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=d,c^2=d,b^a=bd,e^a=e^2f,f^a=ef,g^a=g^2,e^c=e^2,f^c=f^242 conjugacy classes — view the full character table.
| maximal subgroup of | #11722711, #11722713, #11722716, … |
| maximal normal subgroup of | #11722711, #11722713, #11722716, … |
| maximal quotient of | C4⋊(C3⋊#622), #11723102, #11723103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 636);