Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×C7⋊C8 |
| unambiguous semidirect product | (C2×C7)⋊(C8×C13) |
| derived, Sylow | C7 ⋊ C2×C8×C13 |
| Hall | C7×C13 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C13 | D7 |
| commutator, hypocenter | C7 | C2×C8×C13 |
| Frattini | C4 | C2×C13×D7 |
| Fitting | C2×C4×C7×C13 | C2 |
| socle, prime radical | C22×C7×C13 | C4 |
| cosocle | C4×C7 | C22×C13 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C4×C13 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1456 |
520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 53);