Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #441×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3344 |
344 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^82,c^b=cg,d^b=de,h^b=h^82,f^c=fg,h^d=h^82931 conjugacy classes — view the full character table.
| maximal subgroup of | #3344×D83, C2×#24919923, #36283064, … |
| maximal normal subgroup of | #3344×D83, C2×#24919923, #36283064, … |
| maximal quotient of | #35420697, #35420787, #35422076, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16970);