Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#638⋊C3 |
| unambiguous semidirect product | (C2×#638)⋊C3 |
| Fitting | C23×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×D4 |
221 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 15 points:
(3,4)(5,6)(7,8,14)(9,11,13)(10,12,15);(4,6)(8,10)(9,12)(11,13)(14,15);(1,2)62 conjugacy classes — view the full character table.
| maximal subgroup of | #11720333, #63633⋊C3, #11721303, … |
| maximal normal subgroup of | #11720333, #63633⋊C3, #11721303, … |
| maximal quotient of | C2×#3750⋊C3, #64133⋊C3, C2×#3752⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 377);