Finite Group DatabasebetaFinite Group Databasebeta| order | 1360 |
| isoclinism | isoclinic class of #13062853 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C17 ⋊ C16 |
| Sylow | C17 ⋊ #674 |
| Sylow | C5 ⋊ AGL(1,𝔽17) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17 | C16 |
| prime radical | C5×D17 | C8 |
| cosocle | #10621779 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 85 |
Polycyclic presentation:
2^4,5,17|a^2=b,b^2=c,c^2=d,e^a=e^2,f^a=f^3,e^b=e^4,f^b=f^9,f^c=f^13,f^d=f^1625 conjugacy classes — view the full character table.
| maximal subgroup of | #72222280, #72244744, C2×#13062853, … |
| maximal normal subgroup of | #72222280, C2×#13062853 |
| maximal quotient of | #72244744, C2×#13062853, #72244810 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1360, 221);