Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C43 |
| direct product | C2×#11740630 |
| Fitting | C22×C7×#127 ⋊ C2 |
| Sylow | C7 ⋊ C2×#2867 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C22×C7×#127 | C2 |
| socle | C24×C7 | C24 |
| hypercenter | C22×#127 | D7 |
| hypocenter | C7 | C2×#2867 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
8094 conjugacy classes of subgroups; only the 1243 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 1243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 375661);