Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×#11763858 |
| Sylow | C17 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 234 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 | #17951832, #17951833, #17951842, … |
| maximal normal subgroup of | #17951832, #17951833, #17951842, … |
| maximal quotient of | C2×C4⋊C4×#3624, C2×#14544576, C4×#11763858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21292);