Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22⋊C4×C22⋊D83 |
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35419724, #99×C22⋊D83, #35420532, … |
| maximal normal subgroup of | #35419724, #99×C22⋊D83, #35420532, … |
| maximal quotient of | C22⋊C4×(C2×D83)⋊C4, C22⋊C4×C22⋊Dic83, C22⋊C4×Dic83⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7329);