Finite Group DatabasebetaFinite Group Databasebeta| order | 10892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#13095555 |
| Fitting, socle, Hall | C7×C389 ⋊ C4 |
| derived, Sylow | C389 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13095555 |
| commutator, hypocenter | C389 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C389 | C4 |
| prime radical | C7×D389 | C2 |
| cosocle | D389 | C2×C7 |
| LCS | G ▷ C389 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
707 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#13095555, C3×C7×#13095555, C7×C3⋊#13095555 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#13095555, C3×C7×#13095555 |
| maximal quotient of | C3×C7×#13095555, C7×C3⋊#13095555 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10892, 6);