Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C17 ⋊ M128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×#595 |
| commutator, socle | C2×C17 | C2×C32 |
| Fitting | C17×C32 | C4 |
| prime radical | C2×D17 | C32 |
| cosocle | #10587465 | C22 |
| hypercenter | C32 | #595 |
| hypocenter | C17 | M128 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C16 ◁ C32 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^13,h^b=h^16,h^c=h^16208 conjugacy classes — view the full character table.
| maximal subgroup of | #17949546, #17949547, #17949612, … |
| maximal normal subgroup of | #17949546, #17949547, #17949612, … |
| maximal quotient of | #17949545, #17949551, #17949617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19680);