Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting, Sylow | #10624555 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C3×#4169 |
| commutator, cosocle | C32×C9 | C2×C32 |
| Frattini, socle | C33 | C32×D3 |
| Fitting | #10624555 | C2 |
| hypercenter | C32 | #4169 |
| hypocenter | C3×C9 | C2×H(3,𝔽3) |
| LCS | G ▷ C32×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C3 ◁ C32 | |
335 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=g,b^a=bce^2fg^2,c^a=c^2fg^2,e^a=e^2,g^a=g^2,c^b=ce,d^b=df93 conjugacy classes — view the full character table.
| maximal subgroup of | #72221846, #72221854, #72243650, … |
| maximal normal subgroup of | #72221846, #72221854, #72243659, … |
| maximal quotient of | #72221837, C2×#13090639 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 713);