Finite Group DatabasebetaFinite Group Databasebeta| order | 16624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C1039 ⋊ C2 |
| Sylow | C1039 ⋊ SD16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8312 |
Polycyclic presentation:
2^4,1039|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1038,c^b=cd,e^b=e^10384159 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D1039, C2×#30659016, #45685228, … |
| maximal normal subgroup of | SD16×D1039, C2×#30659016, #45685228, … |
| maximal quotient of | #45685129, #45685132, #45685139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16624, 29);