Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C83 ⋊ #2090 |
176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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=eg,b^2=d,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^82,e^c=eg,f^c=fg1174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2090×D83, C2×#24908974, #35433525, … |
| maximal normal subgroup of | #2090×D83, C2×#24908974, #35433525, … |
| maximal quotient of | #35309331, #35309338, #35309345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6021);