Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C17×#537 ⋊ C2 |
| Sylow | C17 ⋊ #3493 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C17×#537 | C2 |
| hypercenter | #537 | D17 |
| hypocenter | C17 | #3493 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #537 | |
1040 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|b^2=g,c^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^16,h^c=h^16220 conjugacy classes — view the full character table.
| maximal subgroup of | #17007139, #17007145, #17007150, … |
| maximal normal subgroup of | #17007139, #17007145, #17007150, … |
| maximal quotient of | #17194392, #17194623, #17194826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18229);