Finite Group DatabasebetaFinite Group Databasebeta| order | 21518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D29⋊C7 |
| unambiguous semidirect product | D29⋊(C7×C53) |
| unambiguous semidirect product | (C29⋊C7)⋊(C2×C53) |
| unambiguous semidirect product | (C53×D29)⋊C7 |
| Fitting, socle, Hall | C29×C53 ⋊ C2×C7 |
| derived, Sylow | C29 ⋊ C2×C7×C53 |
| Hall | C53×C29⋊C7 ⋊ C2 |
| Hall | C53×D29 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×C53 |
| Hall | D29 ⋊ C7×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C2×C7×C53 |
| Frattini | C1 | G |
| Fitting, socle | C29×C53 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1537 |
848 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21518, 11);