Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C17×#121 ⋊ C2 |
| Sylow | C17 ⋊ #3537 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | C2×C17×#121 | C2 |
| hypercenter | C2×#121 | D17 |
| hypocenter | C17 | #3537 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×#121 | |
1270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|b^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^b=h^16262 conjugacy classes — view the full character table.
| maximal subgroup of | #16926592, #16926593, #16926596, … |
| maximal normal subgroup of | #16926592, #16926593, #16926596, … |
| maximal quotient of | #17197094, #17197291, #17197293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18745);