Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11×C25 · Schur multiplier (H2) = C1 |
| direct product | C11×C25×Dic7 |
| unambiguous semidirect product | C7⋊(C4×C11×C25) |
| derived, Sylow | C7 ⋊ C4×C11×C25 |
| Hall | C7×C11×C25 ⋊ C4 |
| Hall | C7×C25 ⋊ C4×C11 |
| Hall | C7×C11 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11×C25 | D7 |
| commutator, hypocenter | C7 | C4×C11×C25 |
| Frattini | C2×C5 | C5×C11×D7 |
| Fitting | C2×C7×C11×C25 | C2 |
| socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C11×C25 | |
36 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×C25×Dic7, C11×C25×Dic21, C11×C25×ΓL(1,𝔽8)⋊C4 |
| maximal normal subgroup of | C3×C11×C25×Dic7, C11×C25×ΓL(1,𝔽8)⋊C4 |
| maximal quotient of | C3×C11×C25×Dic7, C11×C25×Dic21 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 7);