Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | C22⋊#6855 |
| Sylow | C22 ⋊ #6855 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C3×A4 |
| commutator | C22×C3 | C92 |
| Fitting | C22×C32×C9 | C3 |
| socle, prime radical, cosocle | C22×C33 | C32 |
| hypercenter | C32×C9 | A4 |
| hypocenter | C22 | #6855 |
| LCS | G ▷ C22×C3 ▷ C22 | |
| UCS | C1 ◁ C33 ◁ C32×C9 | |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
Polycyclic presentation:
3^5,2^2|a^3=c,b^3=d,b^a=be,f^a=fg,g^a=f180 conjugacy classes — view the full character table.
| derived subgroup of | #14516489 |
| maximal subgroup of | #14516445, #14516489, #14516532, … |
| maximal normal subgroup of | #14516445, #14516489, #14516532, … |
| maximal quotient of | Q8⋊#6855, C2×C22⋊#6855 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 173);