Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D173⋊C32 |
| derived, Sylow | C173 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #10621924 |
| commutator, hypocenter | C173 | C2×C32 |
| Frattini | C8 | C2×#10621924 |
| Fitting | C16×C173 | C4 |
| socle | C2×C173 | C2×C16 |
| prime radical | C2×D173 | C16 |
| cosocle | #14583801 | C22 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,173|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^80,g^b=g^172,g^c=g^172752 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#10621924, #36368669, #36368712, … |
| maximal normal subgroup of | C32×#10621924, #36368669, #36368712, … |
| maximal quotient of | #36368668, #36368677, #36368721, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1480);