Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C17×#124 ⋊ C2 |
| Sylow | C17 ⋊ #2491 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^16,h^d=h^16262 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2491, C2×#14533144, #17203469, … |
| maximal normal subgroup of | D17×#2491, C2×#14533144, #17203469, … |
| maximal quotient of | #16956272, #16956675, #16957422, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 8870);