Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #4179⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #4179⋊D3 |
| Fitting, derived, Sylow | C3×#732 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×#732 | C22 |
| Frattini | C32 | D3×C3⋊D3 |
| socle | C32 | ((C3⋊D3)⋊C3)⋊C2 |
| LCS | G ▷ C3×#732 | |
| UCS | C1 | |
193 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2^2,3^5|e^3=g^2,e^a=e^2g,f^a=f^2,g^a=g^2,c^b=c^2,d^b=d^2,f^b=f^2g,e^c=ef,f^c=fg30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4178⋊C2, C2×#4179⋊D3, #72243768, … |
| maximal normal subgroup of | D3×#4178⋊C2, C2×#4179⋊D3, #72243785 |
| maximal quotient of | #14517054, #14517055, #4179⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 465);