Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ Q8×M16 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,h^a=h^4,d^c=dg,h^c=h^13,h^d=h^16,h^f=h^16130 conjugacy classes — view the full character table.
| maximal subgroup of | #17954048, #17954050, #17954056, … |
| maximal normal subgroup of | #17954048, #17954050, #17954056, … |
| maximal quotient of | C4⋊C4×#63243, #17968563, #17968873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21312);