Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C34 |
No aliases for this group.
| Fitting | C22×C3×H(3,𝔽3) ⋊ C3 |
| Sylow | C22 ⋊ #6911 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
3^5,2^2|c^a=cd,d^a=de,f^a=fg,g^a=f,c^b=ce,d^c=de68 conjugacy classes — view the full character table.
| maximal subgroup of | #10619743⋊C3, #10619755⋊C3, #14518191, … |
| maximal normal subgroup of | #10619743⋊C3, #10619755⋊C3, #14518191, … |
| maximal quotient of | #14517243, C2×#11757837 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 562);