Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#124 ⋊ C4 |
| Sylow | C17 ⋊ #2337 |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^4,c^b=ce,h^b=h^13,h^g=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | #17955284, #17955285, #17955288, … |
| maximal normal subgroup of | #17955284, #17955285, #17955288, … |
| maximal quotient of | #17962981, #17962996, #17963000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21011);