Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2681 |
618 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^82,c^b=cg,d^b=de,h^c=h^82,h^d=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35611348, #35611353, #35611374, … |
| maximal normal subgroup of | #35611348, #35611353, #35611374, … |
| maximal quotient of | #35331728, #35331736, #35331755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 10865);