Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #384×D83 |
| Fitting | #384×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#384 |
888 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 365 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 | #1296×D83, #35294496, #35294506, … |
| maximal normal subgroup of | #1296×D83, #35294496, #35294506, … |
| maximal quotient of | C4⋊#95×D83, #35325627, #384×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6909);