Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ C4⋊#95 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=g,c^2=e,b^a=bd,c^a=ce,h^b=h^13,h^g=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17948655, #17956876, #17956877, … |
| maximal normal subgroup of | #17948655, #17956876, #17956877, … |
| maximal quotient of | (C2×#595)⋊#95, #17949634, #17949635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19687);