Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2848 |
1068 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 201 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=e,b^2=e,b^a=be,c^a=cf,d^a=dg,h^d=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299956, #35299976, #35300116, … |
| maximal normal subgroup of | #35299956, #35299976, #35300116, … |
| maximal quotient of | #35335561, #35335611, #35335621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12794);