Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92209 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92209 |
| Fitting | C2×#6868 ⋊ C2 |
| derived, Sylow | #6868 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92209 |
| commutator, cosocle, hypocenter | #6868 | C22 |
| Frattini | C33 | C2×C3⋊D3 |
| Fitting | C2×#6868 | C2 |
| socle | C2×C32 | #272 |
| LCS | G ▷ #6868 | |
| UCS | C1 ◁ C2 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #92209⋊C4, #14515787, #14515789, … |
| maximal normal subgroup of | #92209⋊C4, #14515787, #14515789, … |
| maximal quotient of | #14516128, C4×#92209, C4⋊#92209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 238);