Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D5×D55 |
| unambiguous semidirect product | (C5×D5)⋊(C7×D11) |
| unambiguous semidirect product | (D5×C11)⋊(C7×D5) |
| Fitting, socle, Hall | C52×C7×C11 ⋊ C22 |
| derived, Hall | C52×C11 ⋊ C22×C7 |
| Hall | C52×C7 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ D52 |
| Sylow | C52 ⋊ C2×C7×D11 |
| Sylow | C11 ⋊ C7×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D5×D55 |
| commutator, hypocenter | C52×C11 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C11 | C22 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C7 | |
96 conjugacy classes of subgroups.
812 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#3874⋊D11, D5×ΓL(1,𝔽8)×D55, C3×C7×D5×D55, … |
| maximal normal subgroup of | D5×ΓL(1,𝔽8)×D55, C3×C7×D5×D55 |
| maximal quotient of | C3×C7×D5×D55, C7×D5×D165, C7×D15×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 107);