Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D29 |
| Fitting | C22×Q8×C29 ⋊ C2 |
| Sylow | C29 ⋊ C23×Q8 |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16819414, #16819425, D29×#391, … |
| maximal normal subgroup of | #16819414, #16819425, D29×#391, … |
| maximal quotient of | C22×C4⋊C4×D29, C2×C4×Q8×D29, C22×#11745249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1372);