Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C17×#106 ⋊ C4 |
| Sylow | C17 ⋊ #1773 |
224 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 90 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=e,b^2=f,c^2=de,d^2=g,b^a=bd,c^a=cg,h^a=h^4,d^b=dg,e^b=eg,h^c=h^13,h^e=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | #17960946, #17961082, C2×#14544592, … |
| maximal normal subgroup of | #17960946, #17961082, C2×#14544592, … |
| maximal quotient of | #17952303, #17952307, #17952310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20318);