Finite Group DatabasebetaFinite Group Databasebeta| order | 37568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #125×D587 |
| Fitting | #125×C587 ⋊ C2 |
| Sylow | C587 ⋊ C2×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D587 |
| commutator, socle, cosocle | C22×C587 | C24 |
| Fitting | #125×C587 | C2 |
| prime radical | C22×D587 | C23 |
| hypercenter | #125 | D587 |
| hypocenter | C587 | C2×#125 |
| LCS | G ▷ C22×C587 ▷ C587 | |
| UCS | C1 ◁ C22 ◁ #125 | |
226 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18784 |
4130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37568, 1068);