Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #564×D79 |
| Fitting | #564×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | #564×C79 | C2 |
| prime radical | C22×D79 | C24 |
| hypercenter | #564 | D79 |
| hypocenter | C79 | C2×#564 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #564 | |
896 conjugacy classes of subgroups.
779 conjugacy classes — view the full character table.
| maximal subgroup of | #1658×D79, #1663×D79, #34269569, … |
| maximal normal subgroup of | #1658×D79, #1663×D79, #34269569, … |
| maximal quotient of | #2382×D79, #34450989, #564×Dic79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18652);