Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×C11⋊#1044 |
| unambiguous semidirect product | C11⋊(C7×#1044) |
| Fitting, socle, Hall | C52×C7×C11 ⋊ C4 |
| derived, Hall | C52×C11 ⋊ C4×C7 |
| Hall | C52×C7 ⋊ Dic11 |
| Hall | C7×C11 ⋊ #1044 |
| Sylow | C52 ⋊ C7×Dic11 |
| Sylow | C11 ⋊ C7×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C11⋊#1044 |
| commutator, hypocenter | C52×C11 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C11 | C4 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C7 | |
64 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C11⋊#64480, ΓL(1,𝔽8)×C11⋊#1044, C3×C7×C11⋊#1044, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×C11⋊#1044, C3×C7×C11⋊#1044 |
| maximal quotient of | C3×C7×C11⋊#1044, C7×C3⋊(C11⋊#1044) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 93);