Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92211 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92211 |
| Fitting | C2×H(3,𝔽3)⋊C9 ⋊ C2 |
| derived, Sylow | H(3,𝔽3)⋊C9 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92211 |
| commutator, cosocle, hypocenter | H(3,𝔽3)⋊C9 | C22 |
| Frattini | C33 | C2×C3⋊D3 |
| Fitting | C2×H(3,𝔽3)⋊C9 | C2 |
| socle | C2×C32 | #272 |
| LCS | G ▷ H(3,𝔽3)⋊C9 | |
| UCS | C1 ◁ C2 | |
211 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 35 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 | #92211⋊C4, #14515794, #14515796, … |
| maximal normal subgroup of | #92211⋊C4, #14515794, #14515796, … |
| maximal quotient of | #14516134, C4×#92211, C4⋊#92211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 240);