Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C17 ⋊ #1436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D17 |
| commutator | C22×C17 | C2×C42 |
| Fitting | C22×C42×C17 | C2 |
| socle, prime radical, cosocle | C24×C17 | C23 |
| hypercenter | C22×C42 | D17 |
| hypocenter | C17 | #1436 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=g,c^2=f,b^a=bd,c^a=ce,h^a=h^16568 conjugacy classes — view the full character table.
| maximal subgroup of | #16925841, D17×#1436, C2×#14527017, … |
| maximal normal subgroup of | #16925841, D17×#1436, C2×#14527017, … |
| maximal quotient of | #16922244, #16922249, #16922250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2743);