Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2989 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^82,c^b=ce,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298300, #35298304, #35298307, … |
| maximal normal subgroup of | #35298300, #35298304, #35298307, … |
| maximal quotient of | #35403223, #35403236, #35403301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13628);