Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×C83⋊C16 |
| Sylow | C83 ⋊ Q8×C16 |
134 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35316167, SD16×C83⋊C16, #35316181, … |
| maximal normal subgroup of | #35316167, SD16×C83⋊C16, #35316181, … |
| maximal quotient of | C4⋊C4×C83⋊C16, #35322021, #35322405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6414);