Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×C8×C22⋊D83 |
| Fitting | C23×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14581706, #35294951, #35297295, … |
| maximal normal subgroup of | C8×#14581706, #35294951, #35297295, … |
| maximal quotient of | C2×C8×#13050575, C2×C8×#13050578, C2×C8×#13050577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13181);