Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#10587547 |
| unambiguous semidirect product | D17⋊(C2×#102) |
| Fitting | C22×D4×C17 ⋊ C4 |
| Sylow | C17 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 258 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 | #17956900, #17956901, #17957307, … |
| maximal normal subgroup of | #17956900, #17956901, #17957307, … |
| maximal quotient of | C22×D4⋊#3624, C2×#14544070, C22×#11763657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21124);