Finite Group DatabasebetaFinite Group Databasebeta| order | 2070 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C3⋊D15 |
| unambiguous semidirect product | C3⋊(C23×D15) |
| unambiguous semidirect product | C5⋊(C3⋊D3×C23) |
| Fitting, socle, Hall | C32×C5×C23 ⋊ C2 |
| derived, Hall | C32×C5 ⋊ C2×C23 |
| Hall | C32×C23 ⋊ D5 |
| Hall | C5×C23 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D5×C23 |
| Sylow | C5 ⋊ C3⋊D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊D15 |
| commutator, cosocle, hypocenter | C32×C5 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C23 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 1035 |
A minimal faithful permutation representation — 3 generators on 34 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,26)(27,28)(30,31)(33,34);(24,25,27,28,26)(32,33,34);(29,30,31)552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×C3⋊D15, D5×C3⋊D3×C23, D115⋊(C3⋊D3), … |
| maximal normal subgroup of | D23×C3⋊D15, D5×C3⋊D3×C23, D115⋊(C3⋊D3), … |
| maximal quotient of | C23×C3⋊Dic15, C2×C23×C3⋊D15, C23×C3⋊D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2070, 19);