Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#389 ⋊ C2 |
| Sylow | C17 ⋊ #2721 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C17×#389 | C2 |
| prime radical | C23×D17 | C23 |
| hypercenter | #389 | D17 |
| hypocenter | C17 | #2721 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #389 | |
434 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=f,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^16,c^b=cg,d^b=de256 conjugacy classes — view the full character table.
| maximal subgroup of | #17241775, #17241782, #17241841, … |
| maximal normal subgroup of | #17241775, #17241782, #17241841, … |
| maximal quotient of | #16962038, #16962162, #16962221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 11405);