Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#131×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3573 |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,f^2=g,e^b=eg,d^c=dg,h^e=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35319851, #35319853, #35319854, … |
| maximal normal subgroup of | #35319851, #35319853, #35319854, … |
| maximal quotient of | #36267822, #36267823, #36267824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19221);