Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×#126×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2718 |
490 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=ef,c^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35611796, #35611809, #35611872, … |
| maximal normal subgroup of | #35611796, #35611809, #35611872, … |
| maximal quotient of | #35332052, #35332067, #35332129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 11354);