Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2969 |
370 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,c^b=cg,h^b=h^82,d^c=dg,h^c=h^82,h^d=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35375309, #35375313, #35375346, … |
| maximal normal subgroup of | #35375309, #35375313, #35375346, … |
| maximal quotient of | #35402667, #35402708, #35402791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13513);