Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#123×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2406 |
864 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=e,c^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 | #35321885, #35321905, #35441771, … |
| maximal normal subgroup of | #35321885, #35321905, #35441771, … |
| maximal quotient of | #35326292, #35327092, #35327182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7842);