Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×C22⋊Dic83 |
| Sylow | C83 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 333 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 | #35300842, #35300846, #35300870, … |
| maximal normal subgroup of | #35300842, #35300846, #35300870, … |
| maximal quotient of | C4⋊C4×C22⋊Dic83, Q8×C83⋊#95, #35325942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7346);