Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | Dic7×C11⋊C25 |
| unambiguous semidirect product | C7⋊(C4×C11⋊C25) |
| unambiguous semidirect product | (C11×Dic7)⋊C25 |
| derived, Hall | C7×C11 ⋊ C4×C25 |
| Hall | C7×C11⋊C25 ⋊ C4 |
| Hall | C11×Dic7 ⋊ C25 |
| Sylow | C11 ⋊ C25×Dic7 |
| Sylow | C7 ⋊ C4×C11⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C5 | D7×C11⋊C5 |
| commutator, hypocenter | C7×C11 | C4×C25 |
| Fitting, socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic7×C11⋊C25, Dic21×C11⋊C25, ΓL(1,𝔽8)⋊C4×C11⋊C25 |
| maximal normal subgroup of | C3×Dic7×C11⋊C25, ΓL(1,𝔽8)⋊C4×C11⋊C25 |
| maximal quotient of | C3×Dic7×C11⋊C25, Dic21×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 3);