Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#595 |
| commutator, socle | C2×C17 | C22×C16 |
| Fitting | C17×M32 | C4 |
| prime radical | #63252 | C8 |
| cosocle | #63214 | C23 |
| hypercenter | M32 | #595 |
| hypocenter | C17 | #2258 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C8 ◁ M32 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^13,c^b=cg,h^b=h^16,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17962870, #17962871, #17962873, … |
| maximal normal subgroup of | #17962870, #17962871, #17962873, … |
| maximal quotient of | #17962552, #17962553, #17962573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20934);