Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128276 |
| Fitting | C2×C4⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#536 |
1512 conjugacy classes of subgroups.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296932, #35319920, #35319925, … |
| maximal normal subgroup of | #35296932, #35319920, #35319925, … |
| maximal quotient of | C2×#24910046, C2×#24910054, C2×#24910084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17828);