Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×D8×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3264 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^16,d^b=de,e^b=eg,e^d=eg253 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3264, C2×#14540264, #17909393, … |
| maximal normal subgroup of | D17×#3264, C2×#14540264, #17909393, … |
| maximal quotient of | #17023671, #17023791, #17023911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15990);