Finite Group DatabasebetaFinite Group Databasebeta| order | 36975 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17×C29 · Schur multiplier (H2) = C5 |
| Fitting, socle, Hall | C52×C17×C29 ⋊ C3 |
| derived, Sylow | C52 ⋊ C3×C17×C29 |
| Hall | C52×C29 ⋊ C3×C17 |
| Hall | C52×C17 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C29 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C3×C17×C29 |
| Frattini | C1 | G |
| Fitting, socle | C52×C17×C29 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C17×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7395 |
5423 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36975, 3);