Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C211 ⋊ C3×C4 |
| Hall | Dic1477 ⋊ C3 |
| Hall | #17984521 ⋊ C4 |
| Sylow | C211 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ (C211⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22579732 |
| commutator, hypocenter | C7×C211 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C211 | C2×C3 |
| prime radical | C2×#17984521 | C2 |
| LCS | G ▷ C7×C211 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5908 |
Polycyclic presentation:
2,3,7,211,2|a^2=e,c^a=c^6,d^a=d^210,c^b=c^2,d^b=d^14504 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 29);