Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128425 |
| Fitting | C2×C4⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#556 |
1112 conjugacy classes of subgroups.
1198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296134, #35296159, #35296506, … |
| maximal normal subgroup of | #35296134, #35296159, #35296506, … |
| maximal quotient of | C2×#24910355, C2×#24910414, C2×#24910422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 18060);