Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #6857 ⋊ C4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2,3,2,3^4|a^2=c,b^3=g^2,d^a=d^2,e^a=e^2g,f^a=f^2,d^b=de,e^b=ef,e^d=eg62 conjugacy classes — view the full character table.
| maximal subgroup of | #92199⋊C4, #92161⋊C4, #14515734, … |
| maximal normal subgroup of | #92199⋊C4, #92161⋊C4, #14515734, … |
| maximal quotient of | #14515622, C2×#11757285 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 10);