Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3480 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D17 |
| commutator, socle, cosocle | C22×C17 | C25 |
| Frattini | C22 | C24×D17 |
| Fitting | C4×#41×C17 | C2 |
| hypercenter | C4×#41 | D17 |
| hypocenter | C17 | #3480 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,h^a=h^16,d^b=df,h^d=h^16370 conjugacy classes — view the full character table.
| maximal subgroup of | #17001205, #17001211, #17001264, … |
| maximal normal subgroup of | #17001205, #17001211, #17001264, … |
| maximal quotient of | #17193715, Q8×#10587558, #17193757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 18108);