Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3547 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Fitting | D4×Q8×C17 | C2 |
| hypercenter | D4×Q8 | D17 |
| hypocenter | C17 | #3547 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1022 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^b=h^16,h^d=h^16238 conjugacy classes — view the full character table.
| maximal subgroup of | #17012355, #17012363, #17012370, … |
| maximal normal subgroup of | #17012355, #17012363, #17012370, … |
| maximal quotient of | #17197166, #17197345, #17197507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18895);