Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C24×C22⋊Dic7 |
| Sylow | C7 ⋊ C24×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C26 | C2×D7 |
| commutator | C2×C7 | C25×C4 |
| Frattini | C22 | C25×D7 |
| Fitting, prime radical | C27×C7 | C2 |
| socle | C26×C7 | C22 |
| cosocle | C22×C7 | C26 |
| hypercenter | C27 | D7 |
| hypocenter | C7 | C24×C22⋊C4 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C26 ◁ C27 | |
43678 conjugacy classes of subgroups; only the 13003 normal subgroups are shown.
This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 13003 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076120);