Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | #108×Dic83 |
| Sylow | C83 ⋊ C4×#108 |
228 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 228 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 | #35319627, #359×Dic83, #35319632, … |
| maximal normal subgroup of | #35319627, #359×Dic83, #35319632, … |
| maximal quotient of | #334×Dic83, #335×Dic83, #35295595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4414);