Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#19099577 |
| derived, Sylow | C317 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11929639 |
| commutator, hypocenter | C317 | C2×C16 |
| Frattini | C4 | C2×#11929639 |
| Fitting | C2×C4×C317 | C4 |
| socle, prime radical | C22×C317 | C8 |
| cosocle | #14579261 | C22 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
664 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19099577, #35204109, #35204111, … |
| maximal normal subgroup of | C4×#19099577, #35204109, #35204111, … |
| maximal quotient of | C4×#19099577, C22⋊#19099577, C4⋊#19099577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 218);