Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C17×#387 ⋊ C2 |
| Sylow | C17 ⋊ #2772 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C17×#387 | C2 |
| prime radical | C23×D17 | C23 |
| hypercenter | #387 | D17 |
| hypocenter | C17 | #2772 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #387 | |
378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=efg,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^16,c^b=cg,d^b=de,h^d=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #17242235, #17242241, #17242300, … |
| maximal normal subgroup of | #17242235, #17242241, #17242300, … |
| maximal quotient of | #16962009, #16962384, #16962662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12039);