Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92159 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92159 |
| Fitting | C2×#6856 ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C22×C3 |
| Sylow | #6856 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4175 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C22×C3 |
| Frattini | C33 | C2×C3×D3 |
| Fitting | C2×#6856 | C2 |
| socle | C2×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
179 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
62 conjugacy classes — view the full character table.
| maximal subgroup of | #92159⋊C4, #14515724, #14515726, … |
| maximal normal subgroup of | #92159⋊C4, #14515724, #14515726, … |
| maximal quotient of | #14515900, C4×#92159, C4⋊#92159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 188);