Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C17×#578 ⋊ C2 |
| Sylow | C17 ⋊ #3586 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D17 |
| commutator, cosocle | C4×C17 | C25 |
| Frattini | C4 | C24×D17 |
| Fitting | C17×#578 | C2 |
| socle | C2×C17 | C23×D4 |
| hypercenter | #578 | D17 |
| hypocenter | C17 | #3586 |
| LCS | G ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1412 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|b^2=g,f^2=g,b^a=bf,e^a=eg,f^a=fg,f^b=fg,d^c=dg,h^c=h^16,h^d=h^16,h^e=h^16217 conjugacy classes — view the full character table.
| maximal subgroup of | #17910582, #17910590, #17910599, … |
| maximal normal subgroup of | #17910582, #17910590, #17910599, … |
| maximal quotient of | #17897897, #17897906, #17898007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19295);