Finite Group DatabasebetaFinite Group Databasebeta| order | 22155 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #17984522⋊C5 |
| Fitting, socle, derived, Hall | C7×C211 ⋊ C3×C5 |
| Hall | C7×C211⋊C5 ⋊ C3 |
| Hall | #17984522 ⋊ C5 |
| Hall | C211⋊C5 ⋊ ΓL(1,𝔽8) |
| Sylow | C211 ⋊ C5×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C211⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C211 | C3×C5 |
| LCS | G ▷ C7×C211 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,7,211|c^a=c^2,d^a=d^196,d^b=d^107123 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#17984522⋊C5, #56004686, #56004690, … |
| maximal normal subgroup of | C2×#17984522⋊C5, #56004686, #56004690, … |
| maximal quotient of | C2×#17984522⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22155, 12);