Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C7×#1437 ⋊ C2 |
| Sylow | C7 ⋊ #13820 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C22×C7 | C22×C42 |
| Fitting | C7×#1437 | C2 |
| socle, cosocle | C24×C7 | C24 |
| prime radical | C23×C22⋊D7 | C22 |
| hypercenter | #1437 | D7 |
| hypocenter | C7 | #13820 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ #1437 | |
2666 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,b^2=h,c^2=fg,d^2=fg,b^a=be,c^a=cf,d^b=de,i^d=i^6268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 91131);