Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C7×C7⋊D7 |
| unambiguous semidirect product | (C2×C7)⋊(C7×D7) |
| Fitting, socle | C2×C73 ⋊ C2 |
| derived | C72 ⋊ C22×C7 |
| Sylow | C73 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C7⋊D7 |
| commutator, cosocle, hypocenter | C72 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C73 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C7 | |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 196 |
364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 36);