Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×Q8×C17 ⋊ C2 |
| Hall | C5×C17 ⋊ #41 |
| Sylow | C17 ⋊ #713 |
| Sylow | C5 ⋊ #63256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D85 |
| commutator, socle, cosocle | C2×C5×C17 | C23 |
| Fitting | C5×Q8×C17 | C2 |
| hypercenter | Q8 | D85 |
| hypocenter | C5×C17 | #41 |
| LCS | G ▷ C2×C5×C17 ▷ C5×C17 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 680 |
Polycyclic presentation:
2^4,5,17|b^2=d,c^2=d,c^a=cd,e^a=e^4,f^a=f^16,c^b=cd220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 213);