Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C17 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D17 |
| commutator, socle | C2×C17 | C24×C4 |
| Fitting, prime radical | C17×#585 | C2 |
| cosocle | C4×C17 | C25 |
| hypercenter | #585 | D17 |
| hypocenter | C17 | #3573 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=f,f^2=g,h^a=h^16,e^b=eg,d^c=dg340 conjugacy classes — view the full character table.
| maximal subgroup of | #17040281, #17040287, #17040292, … |
| maximal normal subgroup of | #17040281, #17040287, #17040292, … |
| maximal quotient of | #17897745, #17897780, #17897961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19222);