Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D35×D55 |
| Fitting, socle, derived, Hall | C52×C7×C11 ⋊ C22 |
| Hall | C52×C11 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ D52 |
| Sylow | C52 ⋊ D7×D11 |
| Sylow | C11 ⋊ D5×D35 |
| Sylow | C7 ⋊ D5×D55 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C11 | C22 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
551 conjugacy classes — view the full character table.
| maximal subgroup of | #37528478, D55×C5⋊AGL(1,𝔽7), C3×D35×D55, … |
| maximal normal subgroup of | D55×C5⋊AGL(1,𝔽7), C3×D35×D55 |
| maximal quotient of | C3×D35×D55, D55×D105, D35×D165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 111);