Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #6869⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#6869⋊C2 |
| unambiguous semidirect product | #6869⋊C22 |
| unambiguous semidirect product | (C2×#6869)⋊C2 |
| Fitting | C2×#6869 ⋊ C2 |
| derived, Sylow | #6869 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #6869⋊C2 |
| commutator, cosocle, hypocenter | #6869 | C22 |
| Frattini | C3×C9 | C2×C3⋊D3 |
| Fitting | C2×#6869 | C2 |
| socle | C2×C3 | #4181 |
| LCS | G ▷ #6869 | |
| UCS | C1 ◁ C2 | |
139 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6869⋊C2, C4⋊(#6869⋊C2), #14516179, … |
| maximal normal subgroup of | C4×#6869⋊C2, C4⋊(#6869⋊C2), #14516179, … |
| maximal quotient of | #6869⋊Q8, C4×#6869⋊C2, C4⋊(#6869⋊C2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 239);