Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×#1438 ⋊ C2 |
| Sylow | C7 ⋊ #15948 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator, socle, cosocle | C24×C7 | C24 |
| Fitting | C7×#1438 | C2 |
| prime radical | C22×#6500 | C2 |
| hypercenter | #1438 | D7 |
| hypocenter | C7 | #15948 |
| LCS | G ▷ C24×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ #1438 | |
3730 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|a^2=eh,b^a=be,c^a=cf,d^a=dh,c^b=cg,d^b=de,i^d=i^6190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 117082);