Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #557×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3364 |
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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=eg,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,d^b=de,f^c=fg1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35394330, #35394339, #35394435, … |
| maximal normal subgroup of | #35394330, #35394339, #35394435, … |
| maximal quotient of | #35421018, #35421196, #35423345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17195);