Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #4175 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92173 |
| Fitting | C2×#6866 ⋊ C2 |
| derived | C33 ⋊ C22×C9 |
| Sylow | #6866 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4175 |
| commutator, hypocenter | C33 | C22×C9 |
| Frattini | C33 | C2×C3×D3 |
| Fitting | C2×#6866 | C2 |
| socle | C2×C32 | (C3⋊D3)⋊C3 |
| prime radical | C2×C3×C3⋊(C3⋊D3) | C3 |
| cosocle | C34 | C22×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C2×C3 | |
202 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | #92173⋊C4, #14515773, #14515775, … |
| maximal normal subgroup of | #92173⋊C4, #14515773, #14515775, … |
| maximal quotient of | #14515942, C4×#92173, C4⋊#92173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 202);