Finite Group DatabasebetaFinite Group Databasebeta| order | 5390 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C7 |
| direct product | C5×C11×C7⋊D7 |
| unambiguous semidirect product | C7⋊(C5×C11×D7) |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C5×C11 |
| Hall | C72×C11 ⋊ C2×C5 |
| Hall | C5×C72 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | C7⋊D7 |
| commutator, hypocenter | C72 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C5×C11 | |
80 conjugacy classes of subgroups.
1430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5390, 23);