Finite Group DatabasebetaFinite Group Databasebeta| order | 22155 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C211 · Schur multiplier (H2) = C1 |
| direct product | C5×ΓL(1,𝔽8)×C211 |
| unambiguous semidirect product | C7⋊(C3×C5×C211) |
| unambiguous semidirect product | (C5×C7)⋊(C3×C211) |
| Fitting, socle, Hall | C5×C7×C211 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C5×C211 |
| Hall | C7×C211 ⋊ C3×C5 |
| Hall | C5×C7 ⋊ C3×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C211 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C3×C5×C211 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C211 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C5×C211 | |
16 conjugacy classes of subgroups.
5275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22155, 6);