Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^c=h^821204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×SD16×D83, C2×#24906260, #35373778, … |
| maximal normal subgroup of | C8×SD16×D83, C2×#24906260, #35373778, … |
| maximal quotient of | #35295167, #35295178, #35295627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3307);