Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#11929623 |
| Fitting | D4×Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | D4×Q8×C79 | C2 |
| prime radical | C2×#11929623 | C22 |
| hypercenter | D4×Q8 | D79 |
| hypocenter | C79 | Q8×#41 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1068 conjugacy classes of subgroups.
1025 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34264246, #34264254, #34264261, … |
| maximal normal subgroup of | #34264246, #34264254, #34264261, … |
| maximal quotient of | C4⋊C4×#11929623, Q8×#14579117, Q8×#14579119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18087);