Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #2325 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator | C22×C17 | C23×C4 |
| Fitting, prime radical | C2×C17×#121 | C2 |
| socle, cosocle | C23×C17 | C24 |
| hypercenter | C2×#121 | D17 |
| hypocenter | C17 | #2325 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^16,c^b=ce,h^b=h^16268 conjugacy classes — view the full character table.
| maximal subgroup of | #16928370, #16928374, #16928391, … |
| maximal normal subgroup of | #16928370, #16928374, #16928391, … |
| maximal quotient of | #16955579, #16955621, #16955671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7215);