Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C17×#548 ⋊ C2 |
| Sylow | C17 ⋊ #3497 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C17×#548 | C2 |
| hypercenter | #548 | D17 |
| hypocenter | C17 | #3497 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #548 | |
1492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=f,c^2=g,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^16,h^e=h^16244 conjugacy classes — view the full character table.
| maximal subgroup of | #17910216, #17910227, #17910231, … |
| maximal normal subgroup of | #17910216, #17910227, #17910231, … |
| maximal quotient of | #17194419, #17194683, #17194685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18278);