Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #340×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1736 |
448 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=f,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1736×D83, C2×#24907181, #35401810, … |
| maximal normal subgroup of | #1736×D83, C2×#24907181, #35401810, … |
| maximal quotient of | #35293864, #35293874, #35293886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4228);