Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #90773 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D232 |
| Fitting | C22×C8×C29 ⋊ C2 |
| Sylow | C29 ⋊ C22×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D116 |
| commutator, cosocle | C4×C29 | C24 |
| Frattini | C4 | C23×D29 |
| Fitting | C22×C8×C29 | C2 |
| socle | C23×C29 | D4 |
| hypercenter | C22×C8 | D29 |
| hypocenter | C29 | C22×D8 |
| LCS | G ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16819839, #16819841, #16820356, … |
| maximal normal subgroup of | #16819839, #16819841, #16820356, … |
| maximal quotient of | C22×#11745169, C22×#11745166, C2×C4×D232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1319);