Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128326 |
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#543 |
1296 conjugacy classes of subgroups.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296214, #35296216, C2×#24906384, … |
| maximal normal subgroup of | #35296214, #35296216, C2×#24906384, … |
| maximal quotient of | C2×#24910074, C2×#24910076, C2×#24910190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17904);