Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#19127786 |
| Fitting | C2×#103×C83 ⋊ C2 |
| 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×#19127786, #35402891, #35402918, … |
| maximal normal subgroup of | C4×#19127786, #35402891, #35402918, … |
| maximal quotient of | C2×#24906260, C2×#24906303, C2×#24906302, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13264);