Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C157 ⋊ #431 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^129,g^b=g^156,g^c=g^156,g^e=g^156664 conjugacy classes — view the full character table.
| maximal subgroup of | #34114963, #34114968, #34114991, … |
| maximal normal subgroup of | #34114963, #34114968, #34114991, … |
| maximal quotient of | #34115851, C4×#19097828, C4×C4⋊#11929441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1568);