Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #440×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3403 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=e,c^2=eg,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,c^b=cg,d^b=de,f^c=fg,h^d=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #3403×D83, C2×#24920552, #36285448, … |
| maximal normal subgroup of | #3403×D83, C2×#24920552, #36285448, … |
| maximal quotient of | #35421291, #35421295, #35423291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17599);