Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128386 |
| Fitting | C22×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#552 |
1124 conjugacy classes of subgroups.
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296101, #35370633, #35370641, … |
| maximal normal subgroup of | #35296101, #35370633, #35370641, … |
| maximal quotient of | C2×#24910319, C2×#24910332, C2×#24910344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18017);