Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #556×D149 |
| Fitting | #556×C149 ⋊ C2 |
| Sylow | C149 ⋊ C2×#556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D149 |
| commutator, socle, cosocle | C22×C149 | C25 |
| Fitting | #556×C149 | C2 |
| prime radical | C2×D4×D149 | C22 |
| hypercenter | #556 | D149 |
| hypocenter | C149 | C2×#556 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C22 ◁ #556 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4768 |
1900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 18052);