Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#611 |
| Fitting | C23×C3×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C2×D9 |
| commutator, cosocle | C2×C9 | C23×C3 |
| Frattini | C2×C3 | C22×C3×D3 |
| Fitting | C23×C3×C9 | C2 |
| socle | C22×C32 | C2×D3 |
| hypercenter | C23×C3 | D9 |
| hypocenter | C9 | C2×C3×D4 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C22×C3 ◁ C23×C3 | |
194 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 18 points:
(3,4,5)(7,9)(10,15,17,16,11,13,12,18,14);(6,7)(8,9)(11,13)(12,16)(14,15)(17,18);(1,2)126 conjugacy classes — view the full character table.
| maximal subgroup of | #11720329, C3×#63365, #11721256, … |
| maximal normal subgroup of | #11720329, C3×#63365, #11721256, … |
| maximal quotient of | C2×C3×Dic9⋊C4, C3×#63486, C2×C3×(C2×D9)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 374);