Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #2994 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,h^a=h^13,c^b=ceg,d^b=dg,h^c=h^16,h^d=h^16,h^f=h^16106 conjugacy classes — view the full character table.
| maximal subgroup of | #17967577, #17967579, #17967597, … |
| maximal normal subgroup of | #17967577, #17967579, #17967597, … |
| maximal quotient of | #17968987, #17969026, #17969049, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21460);