Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C17×#519 ⋊ C2 |
| Sylow | C17 ⋊ #3428 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator | C2×C17 | C24×C4 |
| Fitting | C17×#519 | C2 |
| socle, cosocle | C22×C17 | C25 |
| prime radical | C22×#63256 | C2 |
| hypercenter | #519 | D17 |
| hypocenter | C17 | #3428 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #519 | |
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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|a^2=g,e^2=f,b^a=bf,d^a=df,c^b=cf,h^b=h^16,h^c=h^16,h^e=h^16340 conjugacy classes — view the full character table.
| maximal subgroup of | #17034195, #17035138, #17035157, … |
| maximal normal subgroup of | #17034195, #17035138, #17035157, … |
| maximal quotient of | #17192537, #17192552, #17192556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17712);