Finite Group DatabasebetaFinite Group Databasebeta| order | 10682 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D763 |
| unambiguous semidirect product | C109⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C109 ⋊ C2 |
| Sylow | C109 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C109 | C2 |
| LCS | G ▷ C72×C109 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,7^2,109|b^a=b^6,c^a=c^6,d^a=d^1082672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36319520, D7×D763, C7⋊D7×D109, … |
| maximal normal subgroup of | #36319520, D7×D763, C7⋊D7×D109, … |
| maximal quotient of | C7⋊Dic763, C2×C7⋊D763, C3×C7⋊D763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10682, 6);