Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #541×D79 |
| Fitting | #541×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | #541×C79 | C2 |
| prime radical | C23×D79 | C23 |
| hypercenter | #541 | D79 |
| hypocenter | C79 | C2×#541 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #541 | |
1004 conjugacy classes of subgroups.
902 conjugacy classes — view the full character table.
| maximal subgroup of | #3120×D79, #3123×D79, #3127×D79, … |
| maximal normal subgroup of | #3120×D79, #3123×D79, #3127×D79, … |
| maximal quotient of | #2314×D79, #2320×D79, #2323×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17872);