Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#126×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2512 |
496 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=efg,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^82,h^c=h^82,h^d=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2512×D83, C2×#24912048, #35573550, … |
| maximal normal subgroup of | #2512×D83, C2×#24912048, #35573550, … |
| maximal quotient of | #35326426, #35326782, #35327580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9095);