Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #595 |
| commutator, hypocenter | C17 | C4×C32 |
| Frattini | C2×C8 | C2×#595 |
| Fitting | C2×C16×C17 | C4 |
| socle, prime radical | C22×C17 | C2×C16 |
| cosocle | C2×#63214 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,h^a=h^13,h^b=h^16,h^c=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#3624, #17949088, #17949096, … |
| maximal normal subgroup of | C32×#3624, #17949088, #17949096, … |
| maximal quotient of | #17949087, #17949097, #17949392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19615);