Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C22⋊C81)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×(C22⋊C81)⋊C2 |
| derived | C22⋊C81 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C22⋊C81)⋊C2 |
| commutator, cosocle, hypocenter | C22⋊C81 | C2×C3 |
| Frattini | C27 | C3×S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C32 | D27 |
| LCS | G ▷ C22⋊C81 | |
| UCS | C1 ◁ C3 | |
75 conjugacy classes of subgroups.
| minimal degree | μ(G) = 88 |
| transitive degree | μt(G) = 324 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 827);