Finite Group DatabasebetaFinite Group Databasebeta| order | 21315 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C5×C29×#3861 |
| Fitting, socle, Hall | C5×C72×C29 ⋊ C3 |
| derived, Sylow | C72 ⋊ C3×C5×C29 |
| Hall | C72×C29 ⋊ C3×C5 |
| Hall | C5×C72 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C29 | #3861 |
| commutator, cosocle, hypocenter | C72 | C3×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C29 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C5×C29 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7105 |
2755 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21315, 8);