Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #6878⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#6878⋊C2 |
| unambiguous semidirect product | #6878⋊C22 |
| unambiguous semidirect product | (C2×#6878)⋊C2 |
| Fitting | C2×#6878 ⋊ C2 |
| derived | C92 ⋊ C22×C3 |
| Sylow | #6878 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #6878⋊C2 |
| commutator, cosocle, hypocenter | C92 | C22×C3 |
| Frattini | C3×C9 | C2×C3×D3 |
| Fitting | C2×#6878 | C2 |
| socle | C2×C3 | #4179 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C2 | |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#6878⋊C2, C4⋊(#6878⋊C2), #14516079, … |
| maximal normal subgroup of | C4×#6878⋊C2, C4⋊(#6878⋊C2), #14516079, … |
| maximal quotient of | #6878⋊Q8, C4×#6878⋊C2, C4⋊(#6878⋊C2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 219);