Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11745308 |
| Fitting | C22×Q8×C29 ⋊ C2 |
| Sylow | C29 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 928 |
308 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16819796, #16819801, #16819912, … |
| maximal normal subgroup of | #16819796, #16819801, #16819912, … |
| maximal quotient of | C2×#14271020, C2×#14271034, C2×#14271044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1044);