Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #3164 |
340 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=e,c^2=fg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^c=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35463306, #35463310, #35463317, … |
| maximal normal subgroup of | #35463306, #35463310, #35463317, … |
| maximal quotient of | #35404852, #35407767, #35407781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15044);