Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#117 ⋊ C4 |
| Sylow | C17 ⋊ #2298 |
524 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=g,c^2=e,d^2=f,b^a=be,c^a=cf,h^a=h^4,h^b=h^13,h^g=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17968690, #17968693, #17968694, … |
| maximal normal subgroup of | #17968690, #17968693, #17968694, … |
| maximal quotient of | #17962932, #17962937, #17962940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20972);