Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C34 |
No aliases for this group.
| Fitting | C22×#732 ⋊ C3 |
| Sylow | C22 ⋊ #6911 |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^5,2^2|c^a=ce,f^a=fg,g^a=f,c^b=cd,d^b=de,d^c=de52 conjugacy classes — view the full character table.
| maximal subgroup of | #14518163, #4179⋊A4, #14518241, … |
| maximal normal subgroup of | #14518163, #4179⋊A4, #14518241, … |
| maximal quotient of | #14517216, C2×#11757809 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 534);