Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived | C32×Q8 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C3⋊D3)⋊A4 |
| commutator, Fitting, cosocle, hypocenter | C32×Q8 | C2×C3 |
| Frattini, socle | C2×C3 | D3×A4 |
| LCS | G ▷ C32×Q8 | |
| UCS | C1 ◁ C2 | |
79 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(2,5,3)(6,7,8)(10,15,17,12,13,16)(11,14);(1,7,4,5)(2,3,6,8)(9,10,12)(11,13,16)(14,17,15)Polycyclic presentation:
2,3,2^2,3^2,2|c^2=g,d^2=g,e^a=e^2,f^a=f^2,c^b=cd,d^b=c,e^b=ef,d^c=dg26 conjugacy classes — view the full character table.
| maximal subgroup of | #11722253, #11722256, #11722257, … |
| maximal normal subgroup of | #11722253, #11722256, #11722257, … |
| maximal quotient of | #11720765, C2×#88623, #13047041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 270);