Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊Q8×C157 ⋊ C2 |
| Sylow | C157 ⋊ #456 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=f,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,g^b=g^156,d^c=df1108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34098289, #34098291, #34102157, … |
| maximal normal subgroup of | #34098289, #34098291, #34102157, … |
| maximal quotient of | #34099097, #34099104, #34099109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 731);