Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#11744160 |
| Fitting | C2×C7×H(3,𝔽4) ⋊ C2 |
| Sylow | C7 ⋊ C2×#3558 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D7 |
| commutator, cosocle | C22×C7 | C26 |
| Frattini | C22 | C25×D7 |
| Fitting | C2×C7×H(3,𝔽4) | C2 |
| socle | C23×C7 | C25 |
| hypercenter | C2×H(3,𝔽4) | D7 |
| hypocenter | C7 | C2×#3558 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×H(3,𝔽4) | |
8122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076893);