Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#10587549 |
| Fitting | C4×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C4×#103 |
332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#10587549, #17951985, #17951990, … |
| maximal normal subgroup of | C8×#10587549, #17951985, #17951990, … |
| maximal quotient of | C4×Q8⋊#3624, C4×#11763659, #17951875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20278);