Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C16×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×#3633 |
| commutator, socle | C2×C17 | C82 |
| Fitting | C16×C17 | C8 |
| prime radical | C2×D17 | C4×C8 |
| cosocle | C8×#595 | C22 |
| hypercenter | C16 | #3633 |
| hypocenter | C17 | #1311 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C8 ◁ C16 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=bg,h^b=h^9,h^d=h^13,h^f=h^16112 conjugacy classes — view the full character table.
| maximal subgroup of | #17981337, #17981338, C2×#14545799, … |
| maximal normal subgroup of | #17981337, #17981338, C2×#14545799, … |
| maximal quotient of | #17981090, #17981091, #17981195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21525);