Finite Group DatabasebetaFinite Group Databasebeta| order | 7513 |
| automorphism | ? |
| homology | Abelianization (H1) = C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C683⋊C11 |
| Fitting, socle, derived, Sylow | C683 ⋊ C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C683 | C11 |
| LCS | G ▷ C683 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
11,683|b^a=b^65173 conjugacy classes — view the full character table.
| maximal subgroup of | D683⋊C11, C2×C683⋊C11, C3×C683⋊C11, … |
| maximal normal subgroup of | D683⋊C11, C2×C683⋊C11, C3×C683⋊C11, … |
| maximal quotient of | C2×C683⋊C11, C3×C683⋊C11, C5×C683⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7513, 1);