Finite Group DatabasebetaFinite Group Databasebeta| order | 10676 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C17×C157 ⋊ C4 |
| Sylow | C157 ⋊ #595 |
| Sylow | C17 ⋊ #10597845 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C157 | C4 |
| prime radical, cosocle | D2669 | C2 |
| LCS | G ▷ C17×C157 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,17,157|a^2=b,c^a=c^13,d^a=d^129,c^b=c^16,d^b=d^156671 conjugacy classes — view the full character table.
| maximal subgroup of | #24922676⋊C3, C3×#24922676, C3⋊#24922676 |
| maximal normal subgroup of | #24922676⋊C3, C3×#24922676 |
| maximal quotient of | C3×#24922676, C3⋊#24922676 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10676, 9);