Finite Group DatabasebetaFinite Group Databasebeta| order | 21518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊(D29⋊C7) |
| unambiguous semidirect product | (C29⋊C7)⋊D53 |
| unambiguous semidirect product | D1537⋊C7 |
| Fitting, socle, derived, Hall | C29×C53 ⋊ C2×C7 |
| Hall | C53×C29⋊C7 ⋊ C2 |
| Hall | D1537 ⋊ C7 |
| Hall | C29⋊C7 ⋊ D53 |
| Sylow | C53 ⋊ D29⋊C7 |
| Sylow | C29 ⋊ C7×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C53 | C2×C7 |
| LCS | G ▷ C29×C53 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1537 |
Polycyclic presentation:
2,7,29,53|c^a=c^28,d^a=d^52,c^b=c^16302 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21518, 12);