Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D4×C4⋊#595 |
| Fitting | C4×D4×C17 ⋊ C4 |
| Sylow | C17 ⋊ D4×C4⋊C4 |
776 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #17953996, #17954000, #17954004, … |
| maximal normal subgroup of | #17953996, #17954000, #17954004, … |
| maximal quotient of | C22⋊C4×C4⋊#595, C4⋊C4×C4⋊#595, D4×(C2×#595)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21022);