Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14583801 |
| Sylow | C173 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,173|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^1722792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#14583801, #36351519, #36351521, … |
| maximal normal subgroup of | D4⋊#14583801, #36351519, #36351521, … |
| maximal quotient of | #36351627, #36351633, #36351641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 368);