Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C22×C8×C17 ⋊ C4 |
| Sylow | C17 ⋊ #1812 |
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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=f,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^13,f^c=fg,h^f=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #17948792, #17948793, #17948796, … |
| maximal normal subgroup of | #17948792, #17948793, #17948796, … |
| maximal quotient of | #17953274, #17953275, #17953278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20392);