Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C17×#493 ⋊ C2 |
| Sylow | C17 ⋊ #1721 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10587626 |
| commutator, cosocle | C42×C17 | C23 |
| Frattini | C42 | C22×D17 |
| Fitting | C17×#493 | C2 |
| socle | C22×C17 | #127 |
| hypercenter | #493 | D17 |
| hypocenter | C17 | #1721 |
| LCS | G ▷ C42×C17 ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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|b^2=d,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^16,c^b=cf,h^c=h^16202 conjugacy classes — view the full character table.
| maximal subgroup of | #16947736, D17×#1721, C2×#14528451, … |
| maximal normal subgroup of | #16947736, D17×#1721, C2×#14528451, … |
| maximal quotient of | #16928114, #16934125, #16934133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4177);