Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19127504 |
| Sylow | C83 ⋊ C2×#358 |
232 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 101 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 | #35319612, C4×#19127504, #35319622, … |
| maximal normal subgroup of | #35319612, C4×#19127504, #35319622, … |
| maximal quotient of | C2×#24905426, #35314382, #35314434, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6211);