Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C212 |
No aliases for this group.
| Sylow | C7 ⋊ #14679 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C23×C7 | C23×C4 |
| Fitting, prime radical | C27×C7 | C2 |
| socle, cosocle | C24×C7 | C24 |
| hypercenter | C27 | D7 |
| hypocenter | C7 | #14679 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C27 | |
30862 conjugacy classes of subgroups; only the 1323 normal subgroups are shown.
This group has 30862 conjugacy classes of subgroups — too many to draw. Only its 1323 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=h,b^a=be,c^a=cf,d^a=dg,i^a=i^6472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 100724);