Finite Group DatabasebetaFinite Group Databasebeta| order | 7684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C17×C113 ⋊ C4 |
| Sylow | C113 ⋊ #595 |
| Sylow | C17 ⋊ #90673 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C113 | C4 |
| LCS | G ▷ C17×C113 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,17,113|a^2=b,c^a=c^13,d^a=d^15,c^b=c^16,d^b=d^112484 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#21440227, C3⋊#21440227, C5×#21440227, … |
| maximal normal subgroup of | C3×#21440227, C5×#21440227 |
| maximal quotient of | C3×#21440227, C3⋊#21440227, C5×#21440227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7684, 8);