Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624730 ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #92258 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C2×C32 |
| Frattini | C33 | C32×D3 |
| Fitting | #10624730 | C2 |
| socle | C32 | C3×(C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
800 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18 |
Polycyclic presentation:
2,3^6|b^a=b^2,e^a=e^2g,f^a=f^2,c^b=ce,d^b=df,e^b=eg93 conjugacy classes — view the full character table.
| maximal subgroup of | #72221865, #72221881, #72221931, … |
| maximal normal subgroup of | #72221881, #72221931, C2×#13091036, … |
| maximal quotient of | C2×#13091036, #72277644 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1110);