Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C173 ⋊ #101 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=d,b^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^80,d^b=de,f^d=f^172355 conjugacy classes — view the full character table.
| maximal subgroup of | #26012399, #26012400, #26012401, … |
| maximal normal subgroup of | #26012399, #26012400, #26012401, … |
| maximal quotient of | #26012336, #26012337, #26012348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 207);