Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of (C3⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C9 · Schur multiplier (H2) = C34 |
| direct product | C3×C9×(C3⋊D3)⋊C3 |
| Fitting, Sylow | C3×C9×H(3,𝔽3) ⋊ C2 |
| derived | C32 ⋊ C2×C32×C9 |
662 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 160 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 | #72243489, C3×3−1+2×(C3⋊D3)⋊C3, #72243509, … |
| maximal normal subgroup of | #72243489, C3×3−1+2×(C3⋊D3)⋊C3, #72243509, … |
| maximal quotient of | #72243489, C9×#92262, #72243691 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1431);