Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C7×#2556 ⋊ C2 |
| Sylow | C7 ⋊ #34840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2556 | C2 |
| prime radical | C22×C22⋊D7 | C23 |
| hypercenter | #2556 | D7 |
| hypocenter | C7 | #34840 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2556 | |
1944 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^8,7|a^2=g,c^2=gh,e^2=f,b^a=bf,c^a=cg,i^a=i^6,c^b=ch,d^b=dh,i^d=i^6,i^e=i^6190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 339925);