Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of #89428 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#90001 |
| Sylow | C7 ⋊ C22×#395 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C22×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C24×C7×Q8 | C2 |
| socle, prime radical | C25×C7 | C23 |
| hypercenter | C24×Q8 | D7 |
| hypocenter | C7 | C22×#395 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C25 ◁ C24×Q8 | |
6046 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.
This group has 6046 conjugacy classes of subgroups — too many to draw. Only its 1539 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1792 |
328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 335757);