Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C82×C17 ⋊ C2 |
| Sylow | C17 ⋊ #1712 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10587560 |
| commutator, cosocle | C42×C17 | C23 |
| Frattini | C42 | C22×D17 |
| Fitting | C82×C17 | C2 |
| socle | C22×C17 | #127 |
| hypercenter | C82 | D17 |
| hypocenter | C17 | #1712 |
| LCS | G ▷ C42×C17 ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C82 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=df,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^16550 conjugacy classes — view the full character table.
| maximal subgroup of | #16921054, #16947719, #16948496, … |
| maximal normal subgroup of | #16921054, #16947719, #16948496, … |
| maximal quotient of | #16928105, #16934087, #16937093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4125);