Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×#3624 |
| Sylow | C17 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #101×#3624, #17951841, #103×#3624, … |
| maximal normal subgroup of | #101×#3624, #17951841, #103×#3624, … |
| maximal quotient of | C2×C4⋊C4×#3624, C4×Q8×#3624, C2×#14544837, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21291);