Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1459 |
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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,c^2=g,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294944, C8×#14581706, #35294949, … |
| maximal normal subgroup of | #35294944, C8×#14581706, #35294949, … |
| maximal quotient of | #35292361, #35292364, #35292366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2826);