Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊Dic187 |
| derived, Hall | C112×C17 ⋊ C4 |
| Sylow | C112 ⋊ Dic17 |
| Sylow | C17 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊D187 |
| commutator, hypocenter | C112×C17 | C4 |
| Fitting, socle | C2×C112×C17 | C2 |
| LCS | G ▷ C112×C17 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2,11^2,17,2|a^2=e,b^a=b^10,c^a=c^10,d^a=d^162060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C11⋊Dic187)⋊C3, C3⋊(C11⋊Dic187), C3×C11⋊Dic187 |
| maximal normal subgroup of | (C11⋊Dic187)⋊C3, C3×C11⋊Dic187 |
| maximal quotient of | C3⋊(C11⋊Dic187), C3×C11⋊Dic187 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 17);