Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C8×D4×D83 |
| Fitting | C8×D4×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 | D4⋊C16×D83, #35314109, #35314313, … |
| maximal normal subgroup of | D4⋊C16×D83, #35314109, #35314313, … |
| maximal quotient of | C8×D8×D83, C8×SD16×D83, C8×Q16×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13179);