Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2618 |
632 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=e,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^16352 conjugacy classes — view the full character table.
| maximal subgroup of | #16930390, #16930392, #16930400, … |
| maximal normal subgroup of | #16930390, #16930392, #16930400, … |
| maximal quotient of | #16960685, #16960706, #16960838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 10252);