Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×Q8×D332 |
| Fitting | C2×C4×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×D4×Q8 |
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 621 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296130, #35296133, #35296146, … |
| maximal normal subgroup of | #35296130, #35296133, #35296146, … |
| maximal quotient of | C2×Q8×(C2×D83)⋊C4, C2×C4⋊C4×D332, C2×Q8×C4⋊Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17985);