Finite Group DatabasebetaFinite Group Databasebeta| order | 14883 |
| isoclinism | isoclinic class of C112⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C41 · Schur multiplier (H2) = C11 |
| direct product | C41×C112⋊C3 |
| unambiguous semidirect product | C112⋊(C3×C41) |
| unambiguous semidirect product | (C112×C41)⋊C3 |
| Fitting, socle, Hall | C112×C41 ⋊ C3 |
| derived, Sylow | C112 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C112⋊C3 |
| commutator, cosocle, hypocenter | C112 | C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C112×C41 | C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1353 |
1763 conjugacy classes. The character table is too large to display.
| derived subgroup of | C41⋊#10624391 |
| maximal subgroup of | D41×C112⋊C3, C41×#10624391, C41⋊#10624391, … |
| maximal normal subgroup of | D41×C112⋊C3, C41×#10624391, C41⋊#10624391, … |
| maximal quotient of | C2×C41×C112⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14883, 3);