Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊D3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C37 |
| direct product | C32×C3⋊(C3⋊(C3⋊D3)) |
| unambiguous semidirect product | C3⋊(C32×C3⋊(C3⋊D3)) |
| Fitting, socle, Sylow | C36 ⋊ C2 |
| derived | C34 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊(C3⋊(C3⋊D3)) |
| commutator, cosocle, hypocenter | C34 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C36 | C2 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C32 | |
30224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72227880, #72227885, #72227886, … |
| maximal normal subgroup of | #72227880, #72243411, C32×#92301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1797);