Finite Group DatabasebetaFinite Group Databasebeta| order | 5390 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C5×C72×D11 |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C5×C72 |
| Hall | C72×C11 ⋊ C2×C5 |
| Hall | C5×C11 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C72 | D11 |
| commutator, hypocenter | C11 | C2×C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C72 | |
80 conjugacy classes of subgroups.
1715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5390, 20);