Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C92 · Schur multiplier (H2) = C3×C9 |
| direct product | C9×(C3⋊D3)⋊C9 |
| unambiguous semidirect product | (C3⋊D3)⋊C92 |
| Fitting, Sylow | C9×C32⋊C9 ⋊ C2 |
| derived | C32 ⋊ C2×C92 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | (C3⋊D3)⋊C3 |
| commutator, hypocenter | C32 | C2×C92 |
| Frattini, socle | C33 | C32×D3 |
| Fitting | C9×C32⋊C9 | C2 |
| prime radical | C32×C3⋊D3 | C32 |
| cosocle | C34 | C2×C32 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C3×C9 | |
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#92262, #72243691, #72243699, … |
| maximal normal subgroup of | C9×#92262, #72243691, #72243699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 686);