Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2023 |
326 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 95 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=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,e^c=eg,h^c=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293189, #35293190, #35293199, … |
| maximal normal subgroup of | #35293189, #35293190, #35293199, … |
| maximal quotient of | #35307371, #35307381, #35307411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5643);