Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #3056 |
496 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,d^b=dg,h^b=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35441843, #35441844, #35441865, … |
| maximal normal subgroup of | #35441843, #35441844, #35441865, … |
| maximal quotient of | #35387185, #35387207, #35387229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14142);