Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((((C3⋊D3)⋊C3)⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | ((((C3⋊D3)⋊C3)⋊D3)⋊C3)⋊C2 |
| unambiguous semidirect product | #11757730⋊C2 |
| unambiguous semidirect product | #11757731⋊C2 |
| Fitting, derived, Sylow | C32⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32⋊H(3,𝔽3) | C23 |
| Frattini, socle | C32 | D33 |
| LCS | G ▷ C32⋊H(3,𝔽3) | |
| UCS | C1 | |
631 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 631 conjugacy classes of subgroups — too many to draw. Only its 45 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:
2^3,3^5|f^a=f^2,g^a=g^2,h^a=h^2,d^b=d^2,g^b=g^2,e^c=e^2,h^c=h^2,f^d=fg,f^e=fh42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2342);