Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C214×C4 |
| direct product | C23×C42×D7 |
| Fitting | C23×C42×C7 ⋊ C2 |
| derived, Sylow | C7 ⋊ C24×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C42 | D7 |
| commutator, hypocenter | C7 | C24×C42 |
| Frattini | C22 | C25×D7 |
| Fitting | C23×C42×C7 | C2 |
| socle | C25×C7 | C23 |
| prime radical | C25×D7 | C22 |
| cosocle | C22×C7 | C26 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C23×C42 | |
24030 conjugacy classes of subgroups; only the 13515 normal subgroups are shown.
This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 13515 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076116);