Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C157 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^b=g^1562536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C16×D157, C2×#23757091, #34101890, … |
| maximal normal subgroup of | C4⋊C16×D157, C2×#23757091, #34101890, … |
| maximal quotient of | #34098199, #34098205, #34098213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 367);