Finite Group DatabasebetaFinite Group Databasebeta| order | 6868 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C17×C101 ⋊ C4 |
| Sylow | C101 ⋊ #595 |
| Sylow | C17 ⋊ Dic101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C101 | C4 |
| LCS | G ▷ C17×C101 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,17,101|a^2=b,c^a=c^13,d^a=d^100,c^b=c^16508 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#20293556, C3⋊#20293556, #20293556⋊C5, … |
| maximal normal subgroup of | C3×#20293556, #20293556⋊C5, C5×#20293556 |
| maximal quotient of | C3×#20293556, C3⋊#20293556, C5×#20293556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6868, 10);