Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×C8×D83 |
| Fitting | C2×C4×C8×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C22×C4×C8 |
760 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1273×D83, #35293784, #35293788, … |
| maximal normal subgroup of | #1273×D83, #35293784, #35293788, … |
| maximal quotient of | C2×C82×D83, C2×#322×D83, C8×M16×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12909);