Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2417 |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=ef,b^2=e,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^16358 conjugacy classes — view the full character table.
| maximal subgroup of | #17071909, #17071914, #17071984, … |
| maximal normal subgroup of | #17071909, #17071914, #17071984, … |
| maximal quotient of | #16956227, #16956576, #16957156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7955);