Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2352 |
660 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=f,c^2=f,b^a=be,c^a=cf,d^b=de,h^c=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2352×D83, C2×#24910386, #35563786, … |
| maximal normal subgroup of | #2352×D83, C2×#24910386, #35563786, … |
| maximal quotient of | C22⋊C4×Dic83⋊C4, #35325830, #35325851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7433);