Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D7×#1619 |
| Fitting | C7×#1619 ⋊ C2 |
| Sylow | C7 ⋊ C2×#1619 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D7×#120 |
| commutator, cosocle | C42×C7 | C24 |
| Frattini | C42 | C23×D7 |
| Fitting | C7×#1619 | C2 |
| socle | C22×C7 | C2×#120 |
| hypercenter | #1619 | D7 |
| hypocenter | C7 | C2×#1619 |
| LCS | G ▷ C42×C7 ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1619 | |
1838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#18524 |
| maximal normal subgroup of | D7×#18524 |
| maximal quotient of | D7×#12310, D7×#12314 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 145169);