Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #6873 ⋊ C4 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,b^3=d,d^3=g^2,e^a=e^2,f^a=f^2g,e^b=ef,f^e=fg132 conjugacy classes — view the full character table.
| maximal subgroup of | #14515805, #92214⋊C4, #92184⋊C4, … |
| maximal normal subgroup of | #14515805, #92214⋊C4, #92184⋊C4, … |
| maximal quotient of | #14515643, C2×#11757306 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 31);