Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92180 |
| Fitting | C2×H(3,𝔽3)⋊C9 ⋊ C2 |
| derived | C32×C9 ⋊ C22×C3 |
| Sylow | H(3,𝔽3)⋊C9 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92180 |
| commutator, cosocle, hypocenter | C32×C9 | C22×C3 |
| Frattini | C33 | C2×C3×D3 |
| Fitting | C2×H(3,𝔽3)⋊C9 | C2 |
| socle | C2×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C2 | |
187 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 187 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #92180⋊C4, #14515795, #14515796, … |
| maximal normal subgroup of | #92180⋊C4, #14515795, #14515796, … |
| maximal quotient of | #14515961, C4×#92180, C4⋊#92180, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 209);