Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2344 |
604 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=g,b^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 | #35300829, #35300833, #35300857, … |
| maximal normal subgroup of | #35300829, #35300833, #35300857, … |
| maximal quotient of | #35325809, C22⋊C4×C4⋊Dic83, #35325887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7377);