Finite Group DatabasebetaFinite Group Databasebeta| order | 21315 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C49 · Schur multiplier (H2) = C1 |
| derived, Sylow | C29 ⋊ C3×C5×C49 |
| Hall | C3×C5×C29 ⋊ C49 |
| Hall | C5×C29 ⋊ C3×C49 |
| Hall | C3×C29 ⋊ C5×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C7 | C29⋊C7 |
| commutator, hypocenter | C29 | C3×C5×C49 |
| Frattini | C7 | C3×C5×C29⋊C7 |
| Fitting, socle, prime radical | C3×C5×C7×C29 | C7 |
| cosocle | C7×C29 | C3×C5×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C3×C5×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21315 |
1155 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21315, 2);