Finite Group DatabasebetaFinite Group Databasebeta| order | 15004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C11⋊D11)⋊D31 |
| unambiguous semidirect product | D341⋊D11 |
| Fitting, socle, derived, Hall | C112×C31 ⋊ C22 |
| Sylow | C112 ⋊ C2×D31 |
| Sylow | C31 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C31 | C22 |
| LCS | G ▷ C112×C31 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 682 |
Polycyclic presentation:
2^2,11^2,31|c^a=c^10,e^a=e^30,c^b=c^10,d^b=d^10979 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15004, 21);