Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | D4×#6511 |
| Sylow | C7 ⋊ D4×#131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C24×D7 |
| commutator, socle | C22×C7 | C24×C4 |
| Fitting, prime radical | C7×D4×#41 | C2 |
| cosocle | C2×C4×C7 | C25 |
| hypercenter | D4×#41 | D7 |
| hypocenter | C7 | D4×#131 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ D4×#41 | |
2814 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1033536);