Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19099204 |
| Fitting | C2×C22⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#546 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D79 |
| commutator, cosocle | C22×C79 | C25 |
| Frattini | C22 | C24×D79 |
| Fitting | C2×C22⋊Q8×C79 | C2 |
| socle | C23×C79 | C24 |
| hypercenter | C2×C22⋊Q8 | D79 |
| hypocenter | C79 | C2×#546 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
1900 conjugacy classes of subgroups.
1142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34179959, #34303627, #34303684, … |
| maximal normal subgroup of | #34179959, #34303627, #34303684, … |
| maximal quotient of | C2×#23766220, C2×#23766229, C2×#23766247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17956);