Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88989 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C22×C33 ⋊ C4 |
| Sylow | C33 ⋊ C22⋊C4 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 13 points:
(2,4)(5,6,7)(8,10,13);(1,2)(3,4)(6,7)(8,9)(10,11,13,12)Polycyclic presentation:
2^4,3^3|a^2=c,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 | #11722727, #11722728, #11722770, … |
| maximal normal subgroup of | #11722727, #11722728, #11722770, … |
| maximal quotient of | #11723099, #11723103, #11723105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 641);