Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C17×#585 ⋊ C2 |
| Sylow | C17 ⋊ 2−1+6 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×D17 |
| commutator, socle, cosocle | C2×C17 | C26 |
| Fitting | C17×#585 | C2 |
| hypercenter | #585 | D17 |
| hypocenter | C17 | 2−1+6 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ #585 | |
5796 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.
This group has 5796 conjugacy classes of subgroups — too many to draw. Only its 3201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|c^2=g,d^2=g,b^a=bg,f^a=fg,e^b=eg,d^c=dg,h^e=h^16,h^f=h^16337 conjugacy classes — view the full character table.
| maximal subgroup of | #17183072, #17183074, #17183076, … |
| maximal normal subgroup of | #17183072, #17183074, #17183076, … |
| maximal quotient of | #17940944, #17940946, #17940948, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19323);