Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #362 |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=d,b^2=f,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cef,d^b=df,e^b=ef,g^b=g^82590 conjugacy classes — view the full character table.
| maximal subgroup of | #362×D83, C2×#19127516, #24909209, … |
| maximal normal subgroup of | #362×D83, C2×#19127516, #24909209, … |
| maximal quotient of | C2×#19127516 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 364);