Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#90448 |
| Fitting | C23×C7×D8 ⋊ C2 |
| Sylow | C7 ⋊ C22×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D4×D7 |
| commutator, cosocle | C4×C7 | C26 |
| Frattini | C4 | C25×D7 |
| Fitting | C23×C7×D8 | C2 |
| socle | C23×C7 | C22×D4 |
| hypercenter | C23×D8 | D7 |
| hypocenter | C7 | C22×#576 |
| LCS | G ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C23×D8 | |
11462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1083376);