Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Fitting, Sylow | #10624943 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C3⋊(C3⋊(C3⋊D3)) |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C2×C3 |
| Frattini, socle | C3 | C3×C3⋊(C3⋊(C3⋊D3)) |
| Fitting | #10624943 | C2 |
| prime radical | #92404 | C3 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C9 | |
2130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|f^3=g,b^a=b^2g,c^a=c^2,d^a=d^2,e^a=e^2g,c^b=cg,e^b=eg,d^c=dg138 conjugacy classes — view the full character table.
| maximal subgroup of | #72277519, #72277532 |
| maximal normal subgroup of | #72277519, #72277532 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1792);