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×#3719 |
| Sylow | C33 ⋊ Q16 |
110 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 110 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) = 25 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,14,4,3,5,11,10,12)(2,16,7,6,8,9,13,15)(17,18,19)(21,22)(23,24,25);(1,8,5,2)(3,16,12,9)(4,7,10,13)(6,11,15,14)(20,21,22)(24,25)72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3719, #11722847, #11722848, … |
| maximal normal subgroup of | D3×#3719, #11722847, #11722848, … |
| maximal quotient of | C3×#63566, C3×#63567, C3×#63575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 424);