Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C17×#529 ⋊ C2 |
| Sylow | C17 ⋊ #3460 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Frattini | C22 | C24×D17 |
| Fitting | C17×#529 | C2 |
| hypercenter | #529 | D17 |
| hypocenter | C17 | #3460 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ #529 | |
1140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|b^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^b=h^16,h^c=h^16,h^d=h^16268 conjugacy classes — view the full character table.
| maximal subgroup of | #17000897, #17000899, #17000998, … |
| maximal normal subgroup of | #17000897, #17000899, #17000998, … |
| maximal quotient of | #17193005, #17193029, #17193033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17931);