Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D4×C223 ⋊ C2 |
| Sylow | C223 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,223|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^222,d^b=de1121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28383746, #28383747, #28383751, … |
| maximal normal subgroup of | #28383746, #28383747, #28383751, … |
| maximal quotient of | #28383579, #28383585, #28383620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 172);