Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×D4×C17 ⋊ C4 |
| Sylow | C17 ⋊ #2308 |
1160 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1160 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,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 | #17955460, #17955461, #17955468, … |
| maximal normal subgroup of | #17955460, #17955461, #17955468, … |
| maximal quotient of | #17962968, #17962970, #17962989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20982);