Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | #322×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1450 |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=d,b^2=e,d^2=f,e^2=g,h^a=h^82,c^b=cf,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35313407, #35313411, #35313458, … |
| maximal normal subgroup of | #35313407, #35313411, #35313458, … |
| maximal quotient of | #35293762, #35293788, #35294832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2795);