Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting | C22×C3×H(3,𝔽3) ⋊ C3 |
| Sylow | C22 ⋊ #6856 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|b^a=bc,c^a=cd,f^a=fg,g^a=f,c^b=ce68 conjugacy classes — view the full character table.
| derived subgroup of | #14516493 |
| maximal subgroup of | #14516450, #14516493, #14516537, … |
| maximal normal subgroup of | #14516450, #14516493, #14516537, … |
| maximal quotient of | #14515888, C2×#11757454 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 179);