Finite Group DatabasebetaFinite Group Databasebeta| order | 3060 |
| automorphism | Aut(G) order 587520 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D1530 |
| direct product | C2×D765 |
| unambiguous semidirect product | (C2×C5)⋊D153 |
| unambiguous semidirect product | (C2×C9)⋊D85 |
| unambiguous semidirect product | (C2×C17)⋊D45 |
| Fitting | C2×C5×C9×C17 ⋊ C2 |
| derived, Hall | C5×C9×C17 ⋊ C22 |
| Hall | C9×C17 ⋊ C2×D5 |
| Hall | C5×C17 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D45 |
| Sylow | C9 ⋊ C2×D85 |
| Sylow | C5 ⋊ C2×D153 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D765 |
| commutator, cosocle, hypocenter | C5×C9×C17 | C22 |
| Frattini | C3 | C2×D255 |
| Fitting | C2×C5×C9×C17 | C2 |
| socle | C2×C3×C5×C17 | D3 |
| LCS | G ▷ C5×C9×C17 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1530 |
A minimal faithful permutation representation — 2 generators on 33 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);(4,11)(5,10)(6,9)(7,8)(13,16)(14,15)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)768 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3825, D5×D765, C2×C5×D765, … |
| maximal normal subgroup of | C2×C5×D765, C2×C7×D765, C2×C11×D765, … |
| maximal quotient of | C2×D3825, D5×D765, C2×C5×D765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3060, 36);