Finite Group DatabasebetaFinite Group Databasebeta| order | 7514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C13⋊(C17⋊D17) |
| unambiguous semidirect product | C17⋊D221 |
| Fitting, socle, derived, Hall | C13×C172 ⋊ C2 |
| Sylow | C172 ⋊ D13 |
| Sylow | C13 ⋊ C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C172 | C2 |
| LCS | G ▷ C13×C172 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,17^2|b^a=b^12,c^a=c^16,d^a=d^161880 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28418631, #28418632, #28418633, … |
| maximal normal subgroup of | #28418631, #28418632, #28418633, … |
| maximal quotient of | #28418620, C2×C13⋊(C17⋊D17), C3×C13⋊(C17⋊D17), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7514, 10);