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.
| Fitting | C2×C33×C4 ⋊ C2 |
| Sylow | C33 ⋊ C22⋊C4 |
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:
(1,2,3,4)(6,8)(15,16,17);(5,6)(7,8)(10,11)(13,14)(16,17);(12,13,14);(9,10,11)Polycyclic presentation:
2^4,3^3|b^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 | #11723392, #11723403, #11723411, … |
| maximal normal subgroup of | #11723392, #11723403, #11723411, … |
| maximal quotient of | #11722175, #11722176, #11722179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 506);