Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#103×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3308 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^82,f^c=fg1177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3308×D83, C2×#24919450, #36281169, … |
| maximal normal subgroup of | #3308×D83, C2×#24919450, #36281169, … |
| maximal quotient of | #35419910, #35420748, #35421468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16497);