Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×C22⋊#595 |
| Fitting | C22×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ Q8×C22⋊C4 |
820 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #17954994, #17954995, #17955002, … |
| maximal normal subgroup of | #17954994, #17954995, #17955002, … |
| maximal quotient of | C4⋊C4×C22⋊#595, Q8×(C2×#595)⋊C4, #17963054, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21014);