Finite Group DatabasebetaFinite Group Databasebeta| order | 8228 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C17 ⋊ C4 |
| Sylow | C112 ⋊ Dic17 |
| Sylow | C17 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C17 | C4 |
| LCS | G ▷ C112×C17 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,11^2,17|a^2=b,c^a=c^8d^7,d^a=c^8d^3,e^a=e^16,c^b=c^10,d^b=d^10530 conjugacy classes — view the full character table.
| maximal subgroup of | #37590607, #22551741⋊C3, C3×#22551741, … |
| maximal normal subgroup of | #22551741⋊C3, C3×#22551741 |
| maximal quotient of | C3×#22551741, C3⋊#22551741 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8228, 29);