Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128506 |
| Fitting | C2×#131×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#576 |
1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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 | #35320089, #35320092, #35320099, … |
| maximal normal subgroup of | #35320089, #35320092, #35320099, … |
| maximal quotient of | C2×#24915990, C2×#24916063, C2×#24916297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19263);