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×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2354 |
632 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298584, #35298588, #35298612, … |
| maximal normal subgroup of | #35298584, #35298588, #35298612, … |
| maximal quotient of | #35325825, C4⋊C4×C4⋊Dic83, #35325887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7457);