Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic175 |
| unambiguous semidirect product | C7⋊(C11×Dic25) |
| derived, Hall | C7×C25 ⋊ C4×C11 |
| Hall | C7×C11×C25 ⋊ C4 |
| Hall | C11×C25 ⋊ Dic7 |
| Hall | C7×C11 ⋊ Dic25 |
| Sylow | C25 ⋊ C11×Dic7 |
| Sylow | C7 ⋊ C11×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D175 |
| commutator, hypocenter | C7×C25 | C4×C11 |
| Frattini | C2×C5 | C11×D35 |
| Fitting | C2×C7×C11×C25 | C2 |
| socle | C2×C5×C7×C11 | D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C2×C11 | |
36 conjugacy classes of subgroups.
1958 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic175, C11×Dic525, C11×ΓL(1,𝔽8)⋊Dic25 |
| maximal normal subgroup of | C3×C11×Dic175, C11×ΓL(1,𝔽8)⋊Dic25 |
| maximal quotient of | C3×C11×Dic175, C11×Dic525 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 11);