Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#19127627 |
| Fitting | C22×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#397 |
820 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 237 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 | #35299450, #35299465, #35304625, … |
| maximal normal subgroup of | #35299450, #35299465, #35304625, … |
| maximal quotient of | C2×#24905705, C2×#24905711, C2×#24905722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7735);