Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | M32×Dic83 |
| Sylow | C83 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×Dic83, #35319233, #35319411, … |
| maximal normal subgroup of | #347×Dic83, #35319233, #35319411, … |
| maximal quotient of | M32×C83⋊C8, #35313398, #35313428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6102);