Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D317⋊C8 |
| unambiguous semidirect product | D317⋊(C2×C8) |
| derived, Sylow | C317 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11929639 |
| commutator, hypocenter | C317 | C22×C8 |
| Frattini | C2 | C22×#11929639 |
| Fitting | C2×C4×C317 | C4 |
| socle | C22×C317 | C2×C4 |
| prime radical | C22×D317 | C4 |
| cosocle | Dic317 | C23 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
664 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11929639)⋊C8, #35204096, #35204098, … |
| maximal normal subgroup of | (C2×#11929639)⋊C8, #35204096, #35204098, … |
| maximal quotient of | C2×C4×#14579268, C4×D317⋊C8, D317⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 229);