Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C157 ⋊ C4 |
| Sylow | C157 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,c^2=f,b^a=bc,e^a=ef,g^a=g^28,d^b=df,g^b=g^129,g^d=g^156,g^e=g^156646 conjugacy classes — view the full character table.
| maximal subgroup of | #34115106, #34115107, #34115108, … |
| maximal normal subgroup of | #34115106, #34115107, #34115108, … |
| maximal quotient of | #34114959, #34114962, #34114985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1417);