Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D8×Dic83 |
| Sylow | C83 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 245 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 | #357×Dic83, #35319620, #361×Dic83, … |
| maximal normal subgroup of | #357×Dic83, #35319620, #361×Dic83, … |
| maximal quotient of | C2×D8×C83⋊C8, C2×#24906293, C2×#24906348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13261);