Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×Dic7×C11⋊C5 |
| unambiguous semidirect product | C7⋊(C4×C5×C11⋊C5) |
| unambiguous semidirect product | (C11×Dic7)⋊C52 |
| unambiguous semidirect product | (C5×C11×Dic7)⋊C5 |
| derived, Hall | C7×C11 ⋊ C4×C52 |
| Hall | C5×C7×C11⋊C5 ⋊ C4 |
| Hall | C11×Dic7 ⋊ C52 |
| Sylow | C11 ⋊ C52×Dic7 |
| Sylow | C7 ⋊ C4×C5×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D7×C11⋊C5 |
| commutator, hypocenter | C7×C11 | C4×C52 |
| Frattini | C2 | C5×D7×C11⋊C5 |
| Fitting, socle | C2×C5×C7×C11 | C2×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C2×C5 | |
96 conjugacy classes of subgroups.
350 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C11⋊C5×ΓL(1,𝔽8)⋊C4, C3×C5×Dic7×C11⋊C5, C5×C11⋊C5×Dic21 |
| maximal normal subgroup of | C5×C11⋊C5×ΓL(1,𝔽8)⋊C4, C3×C5×Dic7×C11⋊C5 |
| maximal quotient of | C3×C5×Dic7×C11⋊C5, C5×C11⋊C5×Dic21 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 40);