Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14581818 |
| Fitting | C23×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×AGL(1,ℤ/8) |
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35311131, #35311135, #35311144, … |
| maximal normal subgroup of | #35311131, #35311135, #35311144, … |
| maximal quotient of | C22×#19127706, C22×#19127700, C22×#19127741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19243);