Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×M32×D83 |
| Fitting | C2×M32×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×M32 |
400 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1375×D83, #35319252, #1376×D83, … |
| maximal normal subgroup of | #1375×D83, #35319252, #1376×D83, … |
| maximal quotient of | C2×#346×D83, C4×M32×D83, C2×M32×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17604);