Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#19127792 |
| Sylow | C83 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19127792, #35402899, #35402919, … |
| maximal normal subgroup of | C4×#19127792, #35402899, #35402919, … |
| maximal quotient of | C2×#24906266, C2×#24906309, C2×#24906296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13270);