Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #2357 |
560 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 197 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=g,b^2=ef,c^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^16370 conjugacy classes — view the full character table.
| maximal subgroup of | #16927919, #16927924, #16930244, … |
| maximal normal subgroup of | #16927919, #16927924, #16930244, … |
| maximal quotient of | #16955768, #16955787, #16955812, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7481);