Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D77 |
| unambiguous semidirect product | (C7×D5)⋊(C5×D11) |
| Fitting, socle, Hall | C52×C7×C11 ⋊ C22 |
| derived | C5×C7×C11 ⋊ C22×C5 |
| Hall | C52×C11 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D11 |
| Hall | C7×C11 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D77 |
| Sylow | C11 ⋊ C5×D5×D7 |
| Sylow | C7 ⋊ C5×D5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D77 |
| commutator, hypocenter | C5×C7×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C11 | C22 |
| LCS | G ▷ C5×C7×C11 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
800 conjugacy classes — view the full character table.
| maximal subgroup of | #3874×D77, C5×D5×C11⋊AGL(1,𝔽7), C3×C5×D5×D77, … |
| maximal normal subgroup of | C5×D5×C11⋊AGL(1,𝔽7), C3×C5×D5×D77 |
| maximal quotient of | C3×C5×D5×D77, C5×D15×D77, C5×D5×D231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 86);