Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2924 |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=e,f^2=g,b^a=be,d^c=dg,h^c=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35300717, #35300721, #35300731, … |
| maximal normal subgroup of | #35300717, #35300721, #35300731, … |
| maximal quotient of | #35401898, #35401968, #35402315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13164);