Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #11929441⋊C8 |
| Sylow | C157 ⋊ #322 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^a=g^129,g^c=g^156664 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11929441⋊C8, #34115332, C8×#14578963, … |
| maximal normal subgroup of | C2×#11929441⋊C8, #34115332, C8×#14578963, … |
| maximal quotient of | #34114958, #11929441⋊C16, #34115054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1391);