Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C17 ⋊ C4 |
| Sylow | C17 ⋊ #2315 |
816 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=g,c^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^13,c^b=ce,h^g=h^16124 conjugacy classes — view the full character table.
| maximal subgroup of | #17953940, #17953941, #17954344, … |
| maximal normal subgroup of | #17953940, #17953941, #17954344, … |
| maximal quotient of | #17962974, #17962985, #17963008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20989);