Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2597 |
454 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=eg,b^2=fg,c^2=g,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^16358 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2597, C2×#14534329, #17204931, … |
| maximal normal subgroup of | D17×#2597, C2×#14534329, #17204931, … |
| maximal quotient of | #16956813, #16956936, #16957933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 10055);