Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #416 |
158 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,83|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^82,d^b=df848 conjugacy classes — view the full character table.
| maximal subgroup of | #24907298, #24907301, #24907305, … |
| maximal normal subgroup of | #24907298, #24907301, #24907305, … |
| maximal quotient of | #24907179, C4×#14581713, C4×#14581716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 545);