Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #443 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^156,d^b=df,g^c=g^1561120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34102014, #34102017, #34102019, … |
| maximal normal subgroup of | #34102014, #34102017, #34102019, … |
| maximal quotient of | D8×#11929434, SD16×#11929434, Q16×#11929434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 666);