Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C157 ⋊ C2 |
| Sylow | C157 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,157|b^a=bd,c^a=ce,g^a=g^156,e^b=ef,d^c=df1342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34102118, #34102119, #34102123, … |
| maximal normal subgroup of | #34102118, #34102119, #34102123, … |
| maximal quotient of | #34099054, #34099059, #34099065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 736);