Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #1279 |
208 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 109 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=d,b^2=e,c^2=f,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=ef,h^a=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1279×D83, C2×#24905303, #35293930, … |
| maximal normal subgroup of | #1279×D83, C2×#24905303, #35293930, … |
| maximal quotient of | #35290932, #35290947, #35290953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2350);