Finite Group DatabasebetaFinite Group Databasebeta| order | 15004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊Dic341 |
| unambiguous semidirect product | C31⋊(C11⋊Dic11) |
| derived, Hall | C112×C31 ⋊ C4 |
| Sylow | C112 ⋊ Dic31 |
| Sylow | C31 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊D341 |
| commutator, hypocenter | C112×C31 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C112×C31 | C2 |
| LCS | G ▷ C112×C31 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15004 |
Polycyclic presentation:
2,11^2,31,2|a^2=e,b^a=b^10,c^a=c^10,d^a=d^303754 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15004, 15);