Finite Group DatabasebetaFinite Group Databasebeta| order | 11780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C19×C31 ⋊ C22×C5 |
| Hall | C19×ΓL(1,𝔽32) ⋊ C22 |
| Hall | D19×D31 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×D19 |
| Sylow | C31 ⋊ C2×C5×D19 |
| Sylow | C19 ⋊ C2×D31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C31 | C22×C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
143 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11780, 14);