Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C17×#550 ⋊ C2 |
| Sylow | C17 ⋊ #3488 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C17×#550 | C2 |
| hypercenter | #550 | D17 |
| hypocenter | C17 | #3488 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #550 | |
1658 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^16,h^c=h^16,h^d=h^16,h^e=h^16244 conjugacy classes — view the full character table.
| maximal subgroup of | #17909728, #17909736, #17909749, … |
| maximal normal subgroup of | #17909728, #17909736, #17909749, … |
| maximal quotient of | #17194362, #17194636, #17194658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18178);