Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#123 ⋊ C4 |
| Sylow | C17 ⋊ #2322 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=e,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 | #17960822, #17971232, C2×#14545270, … |
| maximal normal subgroup of | #17960822, #17971232, C2×#14545270, … |
| maximal quotient of | #17962969, #17962984, #17962988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20996);