Finite Group DatabasebetaFinite Group Databasebeta| order | 10682 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C109 · Schur multiplier (H2) = C7 |
| direct product | C7⋊D7×C109 |
| unambiguous semidirect product | C7⋊(D7×C109) |
| Fitting, socle, Hall | C72×C109 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C109 | C7⋊D7 |
| commutator, cosocle, hypocenter | C72 | C2×C109 |
| Frattini | C1 | G |
| Fitting, socle | C72×C109 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C109 | |
40 conjugacy classes of subgroups.
2834 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C109×#5997, #36319521, D72×C109, … |
| maximal normal subgroup of | C109×#5997, #36319521, D72×C109, … |
| maximal quotient of | C109×C7⋊Dic7, C2×C7⋊D7×C109, C3×C7⋊D7×C109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10682, 7);