Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D32×D79 |
| Fitting | D32×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D79 |
| commutator, cosocle | C16×C79 | C23 |
| Frattini | C16 | C22×D79 |
| Fitting | D32×C79 | C2 |
| socle | C2×C79 | C2×D16 |
| hypercenter | D32 | D79 |
| hypocenter | C79 | C2×D32 |
| LCS | G ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
120 conjugacy classes of subgroups.
779 conjugacy classes — view the full character table.
| maximal subgroup of | D64×D79, SD128×D79, #34209325, … |
| maximal normal subgroup of | D64×D79, SD128×D79, #34209325, … |
| maximal quotient of | #1415×D79, #1423×D79, #34208840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6806);