Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of #13091546 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C9 |
No aliases for this group.
| Fitting, Sylow | #10624913 ⋊ C2 |
| derived | C92 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C92 | C2×C32 |
| Frattini, socle | C32 | C32×C3⋊D3 |
| Fitting | #10624913 | C2 |
| LCS | G ▷ C92 | |
| UCS | C1 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=fg,c^3=f^2,b^a=b^2eg^2,c^a=c^2f,d^a=df^2g^2,e^a=eg,f^a=f^2,g^a=g^2,c^b=cf,d^b=dg,e^b=efg,d^c=df^2g,e^c=ef58 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1620);