Finite Group DatabasebetaFinite Group Databasebeta| order | 7700 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C5 |
| direct product | C7×C11×#1044 |
| Fitting, socle, Hall | C52×C7×C11 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C7×C11 |
| Hall | C52×C11 ⋊ C4×C7 |
| Hall | C52×C7 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | #1044 |
| commutator, hypocenter | C52 | C4×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C11 | C4 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C7×C11 | |
64 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C11×#64480, C11×ΓL(1,𝔽8)×#1044, C3×C7×C11×#1044, … |
| maximal normal subgroup of | C11×ΓL(1,𝔽8)×#1044, C3×C7×C11×#1044 |
| maximal quotient of | C3×C7×C11×#1044, C7×C11×C3⋊#1044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7700, 92);