Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#19127704 |
| Fitting | C2×#102×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#418 |
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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 | C4×#19127704, #35402180, #35402212, … |
| maximal normal subgroup of | C4×#19127704, #35402180, #35402212, … |
| maximal quotient of | C2×#24905852, C2×#24905904, #35370841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13009);