Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #417×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3323 |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,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 | #3323×D83, C2×#24919680, #36281355, … |
| maximal normal subgroup of | #3323×D83, C2×#24919680, #36281355, … |
| maximal quotient of | #35420005, #35420808, #35421693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16727);