Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19128131 |
| Fitting | C2×#135×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35321451, #35321452, #35321454, … |
| maximal normal subgroup of | #35321451, #35321452, #35321454, … |
| maximal quotient of | C2×#24909168, C2×#24909170, C2×#24909245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17626);