Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C22×#732 ⋊ C3 |
| Sylow | C22 ⋊ #6908 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^5,2^2|a^3=e,f^a=fg,g^a=f,c^b=cd,d^b=de,d^c=de68 conjugacy classes — view the full character table.
| derived subgroup of | #14518103 |
| maximal subgroup of | #14518032, #14518103, #14518160, … |
| maximal normal subgroup of | #14518032, #14518103, #14518160, … |
| maximal quotient of | #14517213, C2×#11757806 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 531);