Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C7×#389 ⋊ C2 |
| Sylow | C7 ⋊ #13974 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C23×C7 | C23×C4 |
| Fitting | C2×C7×#389 | C2 |
| socle, cosocle | C24×C7 | C24 |
| prime radical | C24×D7 | C23 |
| hypercenter | C2×#389 | D7 |
| hypocenter | C7 | #13974 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#389 | |
1802 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=h,b^2=efh,d^2=e,b^a=be,c^a=cf,d^a=de,i^a=i^6,c^b=cg,i^c=i^6244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 92418);