Finite Group DatabasebetaFinite Group Databasebeta| order | 21460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#10596817 |
| Fitting, socle, Hall | C5×C29×C37 ⋊ C4 |
| derived, Hall | C5×C29 ⋊ C4×C37 |
| Hall | C29×C37 ⋊ Dic5 |
| Hall | C5×C37 ⋊ #1181 |
| Sylow | C29 ⋊ Dic5×C37 |
| Sylow | C5 ⋊ C37×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #10596817 |
| commutator, hypocenter | C5×C29 | C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C37 | C4 |
| prime radical | C5×C37×D29 | C2 |
| cosocle | C5×D29 | C2×C37 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5365 |
1591 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21460, 35);