Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #104×Dic83 |
| Sylow | C83 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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×#104×D83, C2×#104×Dic83, #35402126, … |
| maximal normal subgroup of | C4×#104×D83, C2×#104×Dic83, #35402126, … |
| maximal quotient of | D4⋊C8×Dic83, Q8⋊C8×Dic83, #35295018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4317);