Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C131 ⋊ C2 |
| Sylow | C131 ⋊ B(4,𝔽2) |
198 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|b^a=bd,c^a=ce,g^a=g^130,e^b=ef,d^c=df1121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30667943, #30667944, #30667948, … |
| maximal normal subgroup of | #30667943, #30667944, #30667948, … |
| maximal quotient of | #30664879, #30664884, #30664890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 736);