Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Sylow | C22 ⋊ #6893 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×A4 |
| commutator, socle, cosocle | C22×C32 | C33 |
| Fitting, prime radical | C22×C3×H(3,𝔽3) | C3 |
| hypercenter | C3×H(3,𝔽3) | A4 |
| hypocenter | C22 | #6893 |
| LCS | G ▷ C22×C32 ▷ C22 | |
| UCS | C1 ◁ C32 ◁ C3×H(3,𝔽3) | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|a^3=e,c^a=cd,f^a=fg,g^a=f,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | #14518055, #14518065, #14518255, … |
| maximal normal subgroup of | #14518055, #14518065, #14518255, … |
| maximal quotient of | #14517241, C2×#11757833 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 558);