Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #3714 |
| automorphism | Aut(G) = C22×D32×D4 (order 1152) · Inn(G) = #626 · Out(G) = C24 |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×#3716 |
| Sylow | C33 ⋊ SD16 |
122 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,5,7,2,4,8,3,6)(9,10,11)(13,14)(15,16,17);(2,5)(3,7)(6,8)(12,13,14)(16,17)72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3716, #11722839, #11722841, … |
| maximal normal subgroup of | D3×#3716, #11722839, #11722841, … |
| maximal quotient of | C3×#63563, C3×#63567, C3×#63573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 421);