Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212×C4 |
| direct product | C22×#90425 |
| Fitting | C22×C7×C4⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ C22×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D7 |
| commutator, cosocle | C22×C7 | C26 |
| Frattini | C22 | C25×D7 |
| Fitting | C22×C7×C4⋊Q8 | C2 |
| socle | C24×C7 | C24 |
| hypercenter | C22×C4⋊Q8 | D7 |
| hypocenter | C7 | C22×#555 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊Q8 | |
8710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
268 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076588);