Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (#1088⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#1088⋊D3)⋊C3 |
| Fitting, Sylow | H(5,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C3×#272 | C22×C3 |
| Frattini, socle | C3 | C3×#157⋊D3 |
| Fitting | H(5,𝔽3) | D4 |
| hypocenter | C3×H(3,𝔽3) | C3×D4 |
| LCS | G ▷ C3×#272 ▷ C3×H(3,𝔽3) | |
| UCS | C1 | |
243 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,b^a=bd,e^a=e^2,f^a=fh,g^a=g^2,h^a=h^2,e^b=fh^2,f^b=e^2h,g^c=gh^2,e^d=e^2,f^d=f^2h^2,f^e=fh49 conjugacy classes — view the full character table.
| maximal subgroup of | #72228602 |
| maximal normal subgroup of | #72228602 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3515);