Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#117×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2363 |
688 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=eg,c^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^82,d^b=de1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35424699, #35424706, #35424744, … |
| maximal normal subgroup of | #35424699, #35424706, #35424744, … |
| maximal quotient of | #35325829, #35325930, #35325953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7548);