Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C17×#131 ⋊ C4 |
| Sylow | C17 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#595 |
| commutator, socle | C2×C17 | C22×C42 |
| Fitting | C17×#131 | C4 |
| prime radical | #41×D17 | C22 |
| cosocle | C4×D17 | C24 |
| hypercenter | #131 | #595 |
| hypocenter | C17 | #2875 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ #131 | |
556 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^13,d^c=dg,h^f=h^16148 conjugacy classes — view the full character table.
| maximal subgroup of | #17960749, #17960750, #17968839, … |
| maximal normal subgroup of | #17960749, #17960750, #17968839, … |
| maximal quotient of | #17963998, #17963999, #17964000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21080);