Finite Group DatabasebetaFinite Group Databasebeta| order | 10892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#13095555 |
| Fitting, socle, derived, Hall | C7×C389 ⋊ C4 |
| Sylow | C389 ⋊ Dic7 |
| Sylow | C7 ⋊ #13095555 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C389 | C4 |
| prime radical, cosocle | C7×D389 | C2 |
| LCS | G ▷ C7×C389 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,389|a^2=b,c^a=c^6,d^a=d^115,d^b=d^388689 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊#13095555, C3×C7⋊#13095555, C3⋊(C7⋊#13095555) |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#13095555, C3×C7⋊#13095555 |
| maximal quotient of | C3×C7⋊#13095555, C3⋊(C7⋊#13095555) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10892, 7);