Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11929639 |
| unambiguous semidirect product | D317⋊C42 |
| Fitting | C2×C4×C317 ⋊ C4 |
| derived, Sylow | C317 ⋊ C2×C42 |
108 conjugacy classes of subgroups.
664 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11929639)⋊C8, #35204093, #35204095, … |
| maximal normal subgroup of | (C2×#11929639)⋊C8, #35204093, #35204095, … |
| maximal quotient of | C42×#11929639, C2×(C2×#11929639)⋊C4, #35204159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 222);