Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×Dic58 |
| Sylow | C29 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D29 |
| commutator, socle, prime radical, cosocle | C22×C29 | C24 |
| Fitting | C4×Q8×C29 | C2 |
| hypercenter | C4×Q8 | D29 |
| hypocenter | C29 | Q82 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
305 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16818569, #16818572, #16818631, … |
| maximal normal subgroup of | #16818569, #16818572, #16818631, … |
| maximal quotient of | Q8×#90779, C4⋊C4×Dic58, Q8×C4⋊Dic29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1280);