Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊#4178 |
| unambiguous semidirect product | (C2×C3)⋊#4178 |
| Fitting | C2×C3×#732 ⋊ C2 |
| Sylow | C3×#732 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C22×C3 |
| Frattini | C32 | C2×C3×C3⋊D3 |
| Fitting | C2×C3×#732 | C2 |
| socle | C2×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
228 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | #14516901, #14516902, #14516905, … |
| maximal normal subgroup of | #14516901, #14516902, #14516905, … |
| maximal quotient of | #14517599, C4×C3⋊#4178, C4⋊(C3⋊#4178), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 673);