Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | D4×C13×D7 |
| Fitting | C7×D4×C13 ⋊ C2 |
| Hall | C7×C13 ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×D4×C13 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C13 | C22×D7 |
| commutator, cosocle | C2×C7 | C23×C13 |
| Frattini | C2 | C22×C13×D7 |
| Fitting | C7×D4×C13 | C2 |
| socle | C2×C7×C13 | C23 |
| hypercenter | D4×C13 | D7 |
| hypocenter | C7 | C2×D4×C13 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C13 ◁ D4×C13 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 364 |
325 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 150);