Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×SD16×C103 ⋊ C2 |
| Sylow | C103 ⋊ #450 |
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,103|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,g^c=g^102733 conjugacy classes — view the full character table.
| maximal subgroup of | #450×D103, C2×#20267940, #27204358, … |
| maximal normal subgroup of | #450×D103, C2×#20267940, #27204358, … |
| maximal quotient of | #27194094, #27194111, #27194162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 698);