Finite Group DatabasebetaFinite Group Databasebeta| order | 7742 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C7 |
| direct product | C79×C7⋊D7 |
| unambiguous semidirect product | C7⋊(D7×C79) |
| Fitting, socle, Hall | C72×C79 ⋊ C2 |
| derived, Sylow | C72 ⋊ C2×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | C7⋊D7 |
| commutator, hypocenter | C72 | C2×C79 |
| Frattini | C1 | G |
| Fitting, socle | C72×C79 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C79 | |
40 conjugacy classes of subgroups.
2054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7⋊D7×D79, D72×C79, (C7⋊D7)⋊D79, … |
| maximal normal subgroup of | C7⋊D7×D79, D72×C79, (C7⋊D7)⋊D79, … |
| maximal quotient of | C79×C7⋊Dic7, C2×C79×C7⋊D7, C3×C79×C7⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7742, 9);