Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C17×#322 ⋊ C2 |
| Sylow | C17 ⋊ #1454 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D17 |
| commutator, socle | C22×C17 | C2×C42 |
| Fitting | C17×#322 | C2 |
| prime radical | C22×D17 | C42 |
| cosocle | C42×C17 | C23 |
| hypercenter | #322 | D17 |
| hypocenter | C17 | #1454 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C42 ◁ #322 | |
178 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cfg,c^b=cf,h^b=h^16,h^c=h^16376 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1454, C2×#14527085, #16999956, … |
| maximal normal subgroup of | D17×#1454, C2×#14527085, #16999956, … |
| maximal quotient of | #16923698, #16923714, #16924758, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2811);