Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C17×#540 ⋊ C2 |
| Sylow | C17 ⋊ #3548 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C17×#540 | C2 |
| hypercenter | #540 | D17 |
| hypocenter | C17 | #3548 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #540 | |
1114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|c^2=g,d^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^d=h^16,h^e=h^16214 conjugacy classes — view the full character table.
| maximal subgroup of | #17924653, #17924657, #17924713, … |
| maximal normal subgroup of | #17924653, #17924657, #17924713, … |
| maximal quotient of | #17197172, #17197231, #17197819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18904);