Finite Group DatabasebetaFinite Group Databasebeta| order | 16884 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C67 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C67×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C22×C3)⋊(ΓL(1,𝔽8)×C67) |
| unambiguous semidirect product | (C3×C7)⋊(A4×C67) |
| Fitting, socle | C22×C3×C7×C67 ⋊ C3 |
| derived, Hall | C22×C7 ⋊ C32×C67 |
| Hall | C22×C7×C67 ⋊ C32 |
| Hall | C7×C67 ⋊ C3×A4 |
| Hall | C22×C67 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×A4×C67 |
| Sylow | C22 ⋊ C3×ΓL(1,𝔽8)×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C67 | C22⋊ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×C7 | C32×C67 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C7×C67 | C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C3×C67 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5628 |
2412 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16884, 212);