Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C7×#2933 ⋊ C2 |
| Sylow | C7 ⋊ #60141 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C24×D7 |
| commutator, socle | C22×C7 | C24×C4 |
| Fitting | C7×#2933 | C2 |
| prime radical | D7×#525 | C2 |
| cosocle | C2×C4×C7 | C25 |
| hypercenter | #2933 | D7 |
| hypocenter | C7 | #60141 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #2933 | |
2862 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^8,7|a^2=g,c^2=g,g^2=h,b^a=bf,e^a=eh,d^c=dh,i^e=i^6238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1033490);