Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#104×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3018 |
724 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^82,e^b=eg,f^b=fg,e^c=eg,h^c=h^821180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35410363, #35410368, #35410374, … |
| maximal normal subgroup of | #35410363, #35410368, #35410374, … |
| maximal quotient of | #35376512, #35376563, #35376614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13861);