Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#1084 |
| derived | H(3,𝔽3) ⋊ C4×C9 |
| Sylow | C9×H(3,𝔽3) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C9 | C3⋊D3 |
| commutator, hypocenter | H(3,𝔽3) | C4×C9 |
| Frattini, socle | C2×C32 | C3×C3⋊D3 |
| Fitting | C2×C9×H(3,𝔽3) | C2 |
| prime radical, cosocle | C2×C3×H(3,𝔽3) | C2×C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3×C9 | |
207 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#6188, C9⋊#6188, C9×#6196, … |
| maximal normal subgroup of | C9×#6188, C9⋊#6188, C9×#6196, … |
| maximal quotient of | C9×#6180, C2×C9×#1084 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 327);