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 | C4 | C22×#3633 |
| commutator, socle | C2×C17 | C22×C16 |
| Fitting | M16×C17 | C8 |
| prime radical | #63252 | C8 |
| cosocle | #63216 | C23 |
| hypercenter | M16 | #3633 |
| hypocenter | C17 | #2258 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ M16 | |
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^9,c^b=cg,h^b=h^16,h^d=h^13,h^e=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | #17982808, #17982809, #17982811, … |
| maximal normal subgroup of | #17982808, #17982809, #17982811, … |
| maximal quotient of | #17982728, #17982729, #17982748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21744);