Finite Group DatabasebetaFinite Group Databasebeta| order | 11571 |
| isoclinism | isoclinic class of #87704 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#87704 |
| Fitting, socle, Hall | C7×C19×C29 ⋊ C3 |
| derived, Hall | C7×C19 ⋊ C3×C29 |
| Hall | C19×C29 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C29 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×C29 |
| Sylow | C7 ⋊ C29×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #87704 |
| commutator, cosocle, hypocenter | C7×C19 | C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C29 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
1363 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29×#87704, D29×#87704, C29×#11716321, … |
| maximal normal subgroup of | C2×C29×#87704, D29×#87704, C29×#11716321, … |
| maximal quotient of | C2×C29×#87704, C29×#11924776, C3×C29×#87704 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11571, 5);