Finite Group DatabasebetaFinite Group Databasebeta| order | 7527 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C193 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×C193 |
| unambiguous semidirect product | C13⋊(C3×C193) |
| Fitting, socle, Hall | C13×C193 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C193 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C193 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C193 |
| Frattini | C1 | G |
| Fitting, socle | C13×C193 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C193 | |
8 conjugacy classes of subgroups.
1351 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C13⋊C3×C193, C13⋊C3×D193, D13⋊C3×C193, … |
| maximal normal subgroup of | C2×C13⋊C3×C193, C13⋊C3×D193, D13⋊C3×C193, … |
| maximal quotient of | C2×C13⋊C3×C193, C13⋊C9×C193, C3×C13⋊C3×C193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7527, 1);