Finite Group DatabasebetaFinite Group Databasebeta| order | 16775 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| Fitting, socle, derived, Hall | C11×C61 ⋊ C52 |
| Sylow | C61 ⋊ C5×C11⋊C5 |
| Sylow | C11 ⋊ C5×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C61 | C52 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 671 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | (C11⋊C5)⋊(D61⋊C5), AGL(1,𝔽11)×C61⋊C5, C11⋊C5×D61⋊C5, … |
| maximal normal subgroup of | (C11⋊C5)⋊(D61⋊C5), AGL(1,𝔽11)×C61⋊C5, C11⋊C5×D61⋊C5, … |
| maximal quotient of | C2×C11⋊C5×C61⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16775, 9);