Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×SD16×#595 |
| unambiguous semidirect product | D17⋊(C4×SD16) |
| Fitting | C2×SD16×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×C4×SD16 |
552 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C4×SD16×#595, #440×#595, #17968819, … |
| maximal normal subgroup of | C4×SD16×#595, #440×#595, #17968819, … |
| maximal quotient of | C2×SD16×#3624, C2×#14544367, C2×#14544368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21258);