Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #324 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=ce,d^b=de,g^b=g^1561582 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #324×D157, C2×#23756998, #34098447, … |
| maximal normal subgroup of | #324×D157, C2×#23756998, #34098447, … |
| maximal quotient of | #34097958, #34097960, #34097978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 274);