Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#11739792 |
| Fitting | C22×C4×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ C2×#2397 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C22×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C22×C4×C7×D4 | C2 |
| socle | C24×C7 | C24 |
| hypercenter | C22×C4×D4 | D7 |
| hypocenter | C7 | C2×#2397 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C4×D4 | |
5150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 335832);