Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2638 |
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|c^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^82,d^c=de1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35300364, #35300369, #35378293, … |
| maximal normal subgroup of | #35300364, #35300369, #35378293, … |
| maximal quotient of | #35330890, #35330905, #35331089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 10428);