Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2217 |
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^822662 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2217×D83, C2×#24909559, #35558841, … |
| maximal normal subgroup of | #2217×D83, C2×#24909559, #35558841, … |
| maximal quotient of | #35318620, #35318671, #35318739, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6606);