Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D29 |
| unambiguous semidirect product | C29⋊C26 |
| unambiguous semidirect product | (C2×C29)⋊C25 |
| Fitting, socle | C25×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D29 |
| commutator, cosocle, hypocenter | C29 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×#379, C2×#14271018, #16827768, … |
| maximal normal subgroup of | D29×#379, C2×#14271018, #16827768, … |
| maximal quotient of | C24×C4×D29, C25×Dic29, C23×D4×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1387);