Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×Q8×Dic83 |
| Sylow | C83 ⋊ C42×Q8 |
684 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 425 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⋊C8×Dic83, #35295013, #35295023, … |
| maximal normal subgroup of | Q8⋊C8×Dic83, #35295013, #35295023, … |
| maximal quotient of | C4×C4⋊C4×Dic83, C4×#19127587, #387×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6861);