Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C22×C3×H(3,𝔽3) ⋊ C3 |
| Sylow | C22 ⋊ #6909 |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
3^5,2^2|b^a=be,c^a=cd,f^a=fg,g^a=f,d^c=de68 conjugacy classes — view the full character table.
| maximal subgroup of | #10619745⋊C3, #10619757⋊C3, #14518197, … |
| maximal normal subgroup of | #10619745⋊C3, #10619757⋊C3, #14518197, … |
| maximal quotient of | #14517248, C2×#11757841 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 566);