Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×C22⋊Q8 ⋊ C4 |
| Sylow | C17 ⋊ #2362 |
576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^4,d^b=de,h^b=h^13,h^g=h^16106 conjugacy classes — view the full character table.
| maximal subgroup of | #17976042, #17976047, #17976050, … |
| maximal normal subgroup of | #17976042, #17976047, #17976050, … |
| maximal quotient of | #17963025, #17963051, #17963055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21036);