Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14578929 |
| Sylow | C157 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^1562536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34098059, #34098060, #34098061, … |
| maximal normal subgroup of | #34098059, #34098060, #34098061, … |
| maximal quotient of | #34098060, #34098076, D4⋊#14578929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 329);