Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×C11×Dic5 |
| derived | C5 ⋊ C4×C5×C7×C11 |
| Hall | C52×C7×C11 ⋊ C4 |
| Hall | C52×C11 ⋊ C4×C7 |
| Hall | C52×C7 ⋊ C4×C11 |
| Sylow | C52 ⋊ C4×C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C7×C11 | D5 |
| commutator, hypocenter | C5 | C4×C5×C7×C11 |
| Frattini | C2 | C5×C7×D5×C11 |
| Fitting, socle | C2×C52×C7×C11 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C5×C7×C11 | |
64 conjugacy classes of subgroups.
3080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×Dic5×ΓL(1,𝔽8), C7×C11×#64470, C5×C7×C11×Dic15, … |
| maximal normal subgroup of | C5×C11×Dic5×ΓL(1,𝔽8), C3×C5×C7×C11×Dic5 |
| maximal quotient of | C5×C7×C11×Dic15, C3×C5×C7×C11×Dic5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 49);