Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C11⋊D407) |
| unambiguous semidirect product | C11⋊D1221 |
| unambiguous semidirect product | C37⋊(C3⋊(C11⋊D11)) |
| Fitting, socle, derived, Hall | C3×C112×C37 ⋊ C2 |
| Hall | C112×C37 ⋊ D3 |
| Hall | C3×C112 ⋊ D37 |
| Sylow | C112 ⋊ D111 |
| Hall | C3×C37 ⋊ C11⋊D11 |
| Sylow | C37 ⋊ C3⋊(C11⋊D11) |
| Sylow | C3 ⋊ C11⋊D407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C112×C37 | C2 |
| LCS | G ▷ C3×C112×C37 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13431 |
Polycyclic presentation:
2,3,11^2,37|b^a=b^2,c^a=c^10,d^a=d^10,e^a=e^366717 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 40);