Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C17×#585 ⋊ C2 |
| Sylow | C17 ⋊ #3586 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D17 |
| commutator, cosocle | C4×C17 | C25 |
| Frattini | C4 | C24×D17 |
| Fitting | C17×#585 | C2 |
| socle | C2×C17 | C23×D4 |
| hypercenter | #585 | D17 |
| hypocenter | C17 | #3586 |
| LCS | G ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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,h^b=h^16,d^c=dg313 conjugacy classes — view the full character table.
| maximal subgroup of | #17065626, #17065628, #17065648, … |
| maximal normal subgroup of | #17065626, #17065628, #17065648, … |
| maximal quotient of | #17897900, #17897908, #17898010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19296);