Finite Group DatabasebetaFinite Group Databasebeta| order | 7514 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×D13 |
| unambiguous semidirect product | C13⋊(C2×C172) |
| Fitting, socle, Hall | C13×C172 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C172 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C172 | D13 |
| commutator, hypocenter | C13 | C2×C172 |
| Frattini | C1 | G |
| Fitting, socle | C13×C172 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C172 | |
80 conjugacy classes of subgroups.
2312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C172×#261, C17×#11725132, #28418636, … |
| maximal normal subgroup of | C172×#261, C17×#11725132, #28418636, … |
| maximal quotient of | C172×Dic13, C2×C172×D13, C3×C172×D13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7514, 8);