Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | #10624929 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | #10624929 | C2 |
| socle | C3 | C32×(C3⋊D3)⋊C3 |
| hypercenter | C3×C9 | (C3⋊D3)⋊C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C9 ◁ C3×C9 | |
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|e^3=g,b^a=b^2,f^a=f^2g,c^b=cf,f^b=fg,d^c=dg102 conjugacy classes — view the full character table.
| maximal subgroup of | #72243645, #72243854, #72277524 |
| maximal normal subgroup of | #72243645, #72243854 |
| automorphism group of | #6869 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1715);