Finite Group DatabasebetaFinite Group Databasebeta| order | 15004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D112×C31 |
| unambiguous semidirect product | (C11×D11)⋊(C2×C31) |
| unambiguous semidirect product | (C11⋊D11)⋊(C2×C31) |
| Fitting, socle, Hall | C112×C31 ⋊ C22 |
| derived, Sylow | C112 ⋊ C22×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D112 |
| commutator, cosocle, hypocenter | C112 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C112×C31 | C22 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C31 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 682 |
1519 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15004, 19);