Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2988 |
432 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^b=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298286, #35298290, #35298293, … |
| maximal normal subgroup of | #35298286, #35298290, #35298293, … |
| maximal quotient of | #35403192, #35403194, #35403286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13619);