Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C17 ⋊ #2840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting | C17×#379 | C2 |
| prime radical | C25×C17 | C22 |
| hypercenter | #379 | D17 |
| hypocenter | C17 | #2840 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #379 | |
580 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|b^2=g,c^2=g,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^16250 conjugacy classes — view the full character table.
| maximal subgroup of | #16937574, #16937575, #16937577, … |
| maximal normal subgroup of | #16937574, #16937575, #16937577, … |
| maximal quotient of | #16965112, #16965452, #16965453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 12763);