Finite Group DatabasebetaFinite Group Databasebeta| order | 1776 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×Q8⋊(C37⋊C3) |
| unambiguous semidirect product | (C2×Q8)⋊(C37⋊C3) |
| unambiguous semidirect product | (C2×C37)⋊SL(2,𝔽3) |
| Fitting, Hall | C2×Q8×C37 ⋊ C3 |
| derived | Q8×C37 ⋊ C2×C3 |
| Sylow | C37 ⋊ C2×SL(2,𝔽3) |
| Sylow | C2×Q8 ⋊ C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C22⋊(C37⋊C3) |
| commutator, cosocle, hypocenter | Q8×C37 | C2×C3 |
| Frattini | C2 | C2×C22⋊(C37⋊C3) |
| Fitting | C2×Q8×C37 | C3 |
| socle | C22×C37 | A4 |
| LCS | G ▷ Q8×C37 | |
| UCS | C1 ◁ C22 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1776, 202);