Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | #10624943 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C32×C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C33 |
| Frattini, socle | C3 | C33×C3⋊D3 |
| Fitting | #10624943 | C2 |
| prime radical | #92392 | C3 |
| hypercenter | #737 | C3⋊D3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C9 ◁ #737 | |
1662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|f^3=g,b^a=bce^2g^2,c^a=eg,d^a=b^2d^2eg,e^a=cg^2,c^b=cg,e^b=eg,d^c=dg174 conjugacy classes — view the full character table.
| maximal subgroup of | #72277524, #72277532 |
| maximal normal subgroup of | #72277532 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1791);