Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #432 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,c^2=d,e^2=f,b^a=bd,c^a=cf,g^a=g^129,g^e=g^156652 conjugacy classes — view the full character table.
| maximal subgroup of | #34114987, #34114994, #34115004, … |
| maximal normal subgroup of | #34114987, #34114994, #34115004, … |
| maximal quotient of | #34115853, #34115862, #34115921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1569);