Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×D91 |
| Fitting | C7×D4×C13 ⋊ C2 |
| Hall | C7×C13 ⋊ C2×D4 |
| Sylow | C13 ⋊ D4×D7 |
| Sylow | C7 ⋊ D4×D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D91 |
| commutator, socle, cosocle | C2×C7×C13 | C23 |
| Fitting | C7×D4×C13 | C2 |
| hypercenter | D4 | D91 |
| hypocenter | C7×C13 | C2×D4 |
| LCS | G ▷ C2×C7×C13 ▷ C7×C13 | |
| UCS | C1 ◁ C2 ◁ D4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 364 |
235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 160);