Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11929639 |
| unambiguous semidirect product | D317⋊(C4⋊C4) |
| Fitting | C2×C4×C317 ⋊ C4 |
| Sylow | C317 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
652 conjugacy classes — view the full character table.
| maximal subgroup of | #35204096, #35204097, #35204102, … |
| maximal normal subgroup of | #35204096, #35204097, #35204102, … |
| maximal quotient of | C2×(C2×#11929639)⋊C4, C4×C4⋊#11929639, #35204165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 224);