Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C221 |
| direct product | C25×C4×D7 |
| Fitting | C25×C4×C7 ⋊ C2 |
| derived, Sylow | C7 ⋊ C26×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C4 | D7 |
| commutator, hypocenter | C7 | C26×C4 |
| Frattini | C2 | C26×D7 |
| Fitting | C25×C4×C7 | C2 |
| socle | C26×C7 | C22 |
| prime radical | C26×D7 | C2 |
| cosocle | C2×C7 | C27 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C25×C4 | |
111198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083442);