Finite Group DatabasebetaFinite Group Databasebeta| order | 11110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C11×C101 ⋊ C2×C5 |
| Hall | #19149921 ⋊ C2 |
| Hall | D1111 ⋊ C5 |
| Sylow | C101 ⋊ AGL(1,𝔽11) |
| Sylow | C11 ⋊ D101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C101 | C2×C5 |
| LCS | G ▷ C11×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,101|c^a=c^10,d^a=d^100,c^b=c^4,d^b=d^95121 conjugacy classes — view the full character table.
| maximal subgroup of | #26013190⋊C2, C2×#26013202, C3×#26013202, … |
| maximal normal subgroup of | #26013190⋊C2, C2×#26013202, C3×#26013202 |
| maximal quotient of | #36372467, C2×#26013202, C3×#26013202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11110, 29);