Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C17×#126 ⋊ C2 |
| Sylow | C17 ⋊ #3521 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C2×C17×#126 | C2 |
| hypercenter | C2×#126 | D17 |
| hypocenter | C17 | #3521 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×#126 | |
1042 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|c^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^16268 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3521, C2×#14542844, #17942469, … |
| maximal normal subgroup of | D17×#3521, C2×#14542844, #17942469, … |
| maximal quotient of | #17194549, #17195049, #17195055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18570);