Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1797 |
400 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=d,f^2=g,b^a=bd,c^a=ce,h^c=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295769, #35295773, #35295777, … |
| maximal normal subgroup of | #35295769, #35295773, #35295777, … |
| maximal quotient of | #35297058, #35297062, #35297066, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4487);