Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C83 ⋊ #2372 |
560 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 560 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=eg,c^2=e,d^2=f,b^a=be,c^a=cf,h^a=h^82,d^b=de,h^b=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35302021, #35302024, #35302031, … |
| maximal normal subgroup of | #35302021, #35302024, #35302031, … |
| maximal quotient of | #35325857, #35325937, #35326008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7622);