Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | (C2×D83)⋊#95 |
| Fitting | C2×#95×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22⋊#95 |
1088 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=g,b^a=bd,c^a=ce,h^c=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295843, #35295847, #35295856, … |
| maximal normal subgroup of | #35295843, #35295847, #35295856, … |
| maximal quotient of | #35292323, #35292325, #35292330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2731);