Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128341 |
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#546 |
1900 conjugacy classes of subgroups.
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35370584, #35370590, #35370664, … |
| maximal normal subgroup of | #35370584, #35370590, #35370664, … |
| maximal quotient of | C2×C22⋊C4×C22⋊D83, C2×#24910290, C2×#24910306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17955);