Finite Group DatabasebetaFinite Group Databasebeta| order | 1380 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic15 |
| unambiguous semidirect product | C3⋊(Dic5×C23) |
| derived, Hall | C3×C5 ⋊ C4×C23 |
| Hall | C3×C5×C23 ⋊ C4 |
| Hall | C5×C23 ⋊ Dic3 |
| Hall | C3×C23 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic3×C23 |
| Sylow | C3 ⋊ Dic5×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D15 |
| commutator, hypocenter | C3×C5 | C4×C23 |
| Frattini | C2 | C23×D15 |
| Fitting, socle, prime radical | C2×C3×C5×C23 | C2 |
| cosocle | C2×C3×C5 | C2×C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C23 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1380 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,27)(28,29,30)(31,32,33,34,35);(24,26,25,27)(29,30)(32,35)(33,34)414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×Dic45, C3×C23×Dic15, C23×C3⋊Dic15, … |
| maximal normal subgroup of | C3×C23×Dic15, C11×C23×Dic15, Dic15×C23⋊C11, … |
| maximal quotient of | C23×Dic45, C3×C23×Dic15, C23×C3⋊Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1380, 6);