Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2728 |
512 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=ef,d^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 | #35612237, #35612239, #35612252, … |
| maximal normal subgroup of | #35612237, #35612239, #35612252, … |
| maximal quotient of | #35332172, #35332174, #35332523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 11477);