Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D317⋊C16 |
| derived, Sylow | C317 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #11929639 |
| commutator, hypocenter | C317 | C2×C16 |
| Frattini | C4 | C2×#11929639 |
| Fitting | C8×C317 | C4 |
| socle | C2×C317 | C2×C8 |
| prime radical | C2×D317 | C8 |
| cosocle | #14579261 | C22 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=c,c^2=d,d^2=e,f^a=f^203,f^b=f^316,f^c=f^316664 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11929639, #35204110, #35204135, … |
| maximal normal subgroup of | C16×#11929639, #35204110, #35204135, … |
| maximal quotient of | #35204109, #35204118, #35204144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 219);