Finite Group DatabasebetaFinite Group Databasebeta| order | 17004 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C109 ⋊ C3×C4 |
| Hall | C13×Dic109 ⋊ C3 |
| Hall | #16862572 ⋊ C4 |
| Hall | Dic109 ⋊ C13⋊C3 |
| Sylow | C109 ⋊ C4×C13⋊C3 |
| Sylow | C13 ⋊ Dic109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22555179 |
| commutator, hypocenter | C13×C109 | C3×C4 |
| Fitting, socle, cosocle | C2×C13×C109 | C2×C3 |
| prime radical | C2×#16862572 | C2 |
| LCS | G ▷ C13×C109 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5668 |
Polycyclic presentation:
2,3,13,109,2|a^2=e,d^a=d^108,c^b=c^3,d^b=d^63496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17004, 15);