Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×Q8⋊#3624 |
| Sylow | C17 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q8⋊#3624, #17951863, #17951869, … |
| maximal normal subgroup of | C4×Q8⋊#3624, #17951863, #17951869, … |
| maximal quotient of | C2×#14543602, C2×#14543604, #17949649, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 19798);