Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1927 |
254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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=f,b^2=dfg,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^82,h^b=h^82,e^c=eg,h^c=h^821186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1927×D83, C2×#24908100, #35406800, … |
| maximal normal subgroup of | #1927×D83, C2×#24908100, #35406800, … |
| maximal quotient of | #35302594, #35302622, #35302748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5147);