Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×C4×Dic166 |
| Sylow | C83 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups; only the 981 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 981 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295747, #35295774, #35295776, … |
| maximal normal subgroup of | #35295747, #35295774, #35295776, … |
| maximal quotient of | C22×C4×C4⋊Dic83, C22×C4×Dic83⋊C4, C2×C42×Dic166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17685);