Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting | C22×C32⋊C9 ⋊ C3 |
| Sylow | C22 ⋊ H(3,𝔽3)⋊C9 |
117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|b^3=c,b^a=bd,d^a=de,f^a=fg,g^a=f,d^b=de84 conjugacy classes — view the full character table.
| derived subgroup of | #11757409⋊C2 |
| maximal subgroup of | #11757409⋊C2, C2×#11757409 |
| maximal normal subgroup of | #11757409⋊C2, C2×#11757409 |
| maximal quotient of | #14515840, C2×#11757409 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 134);