Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C173 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | #10621924 |
| commutator, hypocenter | C173 | C64 |
| Fitting | C16×C173 | C4 |
| socle, prime radical | C2×C173 | C32 |
| cosocle | #19149585 | C2 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C16 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,173|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^80,g^b=g^172752 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#26012330, D173⋊C64, #36368732, … |
| maximal normal subgroup of | C2×#26012330, D173⋊C64, #36368732, … |
| maximal quotient of | #36368378, C2×#26012330 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1388);