Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C8×Q8×D83 |
| Fitting | C8×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 241 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 | Q8⋊C16×D83, #35314209, #35314345, … |
| maximal normal subgroup of | Q8⋊C16×D83, #35314209, #35314345, … |
| maximal quotient of | C8×C4⋊C4×D83, C8×#14581757, C8×Q8×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13429);