Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
| direct product | Q8×C7⋊#95 |
| Sylow | C7 ⋊ Q8×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C22×C7 | C22×C42 |
| Fitting | C22×C4×C7×Q8 | C2 |
| socle, prime radical, cosocle | C24×C7 | C24 |
| hypercenter | C22×C4×Q8 | D7 |
| hypocenter | C7 | Q8×#95 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C22×C4×Q8 | |
2434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1792 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 91054);