Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C22×C32×C9 ⋊ C3 |
| Sylow | C22 ⋊ C9⋊H(3,𝔽3) |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|b^3=e,b^a=be,c^a=cd,f^a=fg,g^a=f132 conjugacy classes — view the full character table.
| maximal subgroup of | #14518182, #14518183, #14518254, … |
| maximal normal subgroup of | #14518182, #14518183, #14518254, … |
| maximal quotient of | #14517237, C2×#11757830 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 555);