Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | #10624930 ⋊ C2 |
| derived | H(5,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C3 | C3⋊(C3⋊((C3⋊D3)⋊C3)) |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C2×C3 |
| Frattini | C32 | C3×C3⋊(C3⋊D3) |
| Fitting | #10624930 | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|b^a=b^2,d^a=d^2,e^a=e^2g^2,f^a=f^2g,c^b=cf,f^b=fg,e^d=eg66 conjugacy classes — view the full character table.
| maximal subgroup of | #72221865, #72221874, #72221878, … |
| maximal normal subgroup of | #72221865, #72221874, #72221878, … |
| maximal quotient of | C2×#13091646 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1720);