Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D85⋊Q8 |
| Hall | C5×C17 ⋊ C2×Q8 |
| Sylow | C17 ⋊ Q8×D5 |
| Sylow | C5 ⋊ Q8×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×D17 |
| commutator, socle, cosocle | C2×C5×C17 | C23 |
| Fitting | C4×C5×C17 | C22 |
| prime radical | C2×D85 | C22 |
| hypercenter | C4 | D5×D17 |
| hypocenter | C5×C17 | C2×Q8 |
| LCS | G ▷ C2×C5×C17 ▷ C5×C17 | |
| UCS | C1 ◁ C2 ◁ C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 680 |
Polycyclic presentation:
2^4,5,17|a^2=d,b^2=d,c^2=d,c^a=cd,f^a=f^16,c^b=cd,e^b=e^4124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 165);