Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2545 |
576 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 165 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=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35322734, #35438697, #35438701, … |
| maximal normal subgroup of | #35322734, #35438697, #35438701, … |
| maximal quotient of | #35326669, #35326962, #35327579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9487);