Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×SD16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2946 |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,e^2=g,b^a=be,e^a=eg,e^b=eg,d^c=dg,h^c=h^82,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2946×D83, C2×#24916290, #36268518, … |
| maximal normal subgroup of | #2946×D83, C2×#24916290, #36268518, … |
| maximal quotient of | #35373837, #35374028, #35374057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13337);