Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#14581772 |
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×C22⋊Q8 |
656 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298924, #35298929, #35298944, … |
| maximal normal subgroup of | #35298924, #35298929, #35298944, … |
| maximal quotient of | C4×#19127575, C4×#19127586, C4×#19127600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7047);