Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #10624755⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624755⋊C2 |
| Fitting, derived, Sylow | #10624755 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #10624755 | C2 |
| Frattini | C33 | C3⋊(C3⋊D3) |
| socle | C3 | #92338 |
| LCS | G ▷ #10624755 | |
| UCS | C1 | |
329 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 329 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|c^3=g,b^a=b^2,c^a=c^2g^2,d^a=d^2,e^a=eg,f^a=fg^2,g^a=g^2,c^b=ce,d^b=df,e^b=eg,f^b=fg,e^c=eg42 conjugacy classes — view the full character table.
| maximal subgroup of | #72221901, #72221912, C2×#10624755⋊C2 |
| maximal normal subgroup of | #72221912, C2×#10624755⋊C2 |
| maximal quotient of | C2×#10624755⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1208);