Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11763808 |
| Fitting | C22×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C2×#421 |
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #17956861, #17956869, #17956884, … |
| maximal normal subgroup of | #17956861, #17956869, #17956884, … |
| maximal quotient of | C2×#14544085, C2×#14544086, C2×#14544082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21139);