Finite Group DatabasebetaFinite Group Databasebeta| order | 16005 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived, Hall | C11×C97 ⋊ C3×C5 |
| Hall | C11⋊C5×C97 ⋊ C3 |
| Hall | C11×C97⋊C3 ⋊ C5 |
| Sylow | C97 ⋊ C3×C11⋊C5 |
| Sylow | C11 ⋊ C5×C97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C97 | C3×C5 |
| LCS | G ▷ C11×C97 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1067 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C11⋊C5×C97⋊C3, C11⋊C5×D97⋊C3, AGL(1,𝔽11)×C97⋊C3, … |
| maximal normal subgroup of | C2×C11⋊C5×C97⋊C3, C11⋊C5×D97⋊C3, AGL(1,𝔽11)×C97⋊C3, … |
| maximal quotient of | C2×C11⋊C5×C97⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16005, 4);