Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Sylow | C7 ⋊ #62653 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D7 |
| commutator | C2×C7 | C25×C4 |
| Fitting, prime radical | C22×C7×2−1+4 | C2 |
| socle, cosocle | C22×C7 | C26 |
| hypercenter | C22×2−1+4 | D7 |
| hypocenter | C7 | #62653 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C22×2−1+4 | |
10930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=h,c^2=g,d^2=g,b^a=bg,f^a=fg,i^a=i^6,e^b=eg,d^c=dg334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076191);