Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #427×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#135 |
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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=f,c^2=f,d^2=g,e^2=g,b^a=be,e^a=eg,e^b=eg,h^b=h^82,h^c=h^821204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319627, #35319632, #35319651, … |
| maximal normal subgroup of | #35319627, #35319632, #35319651, … |
| maximal quotient of | #35373781, #35373933, #35374152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13281);