Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2401 |
432 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=fg,b^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35412659, #35412664, #35412666, … |
| maximal normal subgroup of | #35412659, #35412664, #35412666, … |
| maximal quotient of | #35326101, #35326105, #35326107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7810);