Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×(C22⋊D83)⋊C8 |
| Fitting | C2×C22⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294944, #35294949, #35297297, … |
| maximal normal subgroup of | #35294944, #35294949, #35297297, … |
| maximal quotient of | C2×#24906255, C2×#24906260, C2×#24906266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13180);