Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #400×D79 |
| Fitting | #400×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #400×C79 | C2 |
| prime radical | C23×D79 | C23 |
| hypercenter | #400 | D79 |
| hypocenter | C79 | C2×#400 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #400 | |
604 conjugacy classes of subgroups.
902 conjugacy classes — view the full character table.
| maximal subgroup of | #1353×D79, #34199001, #1615×D79, … |
| maximal normal subgroup of | #1353×D79, #34199001, #1615×D79, … |
| maximal quotient of | #1441×D79, #1442×D79, #1443×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7760);