Finite Group DatabasebetaFinite Group Databasebeta| order | 21515 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C331⋊C5 |
| unambiguous semidirect product | C331⋊(C5×C13) |
| unambiguous semidirect product | (C13×C331)⋊C5 |
| Fitting, socle, Hall | C13×C331 ⋊ C5 |
| derived, Sylow | C331 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C331⋊C5 |
| commutator, cosocle, hypocenter | C331 | C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C331 | C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4303 |
923 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21515, 1);