Finite Group DatabasebetaFinite Group Databasebeta| order | 21730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D41⋊C5 |
| unambiguous semidirect product | D41⋊(C5×C53) |
| unambiguous semidirect product | (C41⋊C5)⋊(C2×C53) |
| unambiguous semidirect product | (C53×D41)⋊C5 |
| Fitting, socle, Hall | C41×C53 ⋊ C2×C5 |
| derived, Sylow | C41 ⋊ C2×C5×C53 |
| Hall | C53×C41⋊C5 ⋊ C2 |
| Hall | C53×D41 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×C53 |
| Hall | D41 ⋊ C5×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C2×C5×C53 |
| Frattini | C1 | G |
| Fitting, socle | C41×C53 | C2×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C53 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2173 |
742 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21730, 11);