Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128294 |
| Fitting | C2×#123×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#539 |
1144 conjugacy classes of subgroups.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35370432, #35370551, C4×#19128294, … |
| maximal normal subgroup of | #35370432, #35370551, C4×#19128294, … |
| maximal quotient of | C2×#24910062, C2×#24910092, C2×#24910093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17857);