Finite Group DatabasebetaFinite Group Databasebeta| order | 4524 |
| automorphism | Aut(G) order 1520064 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2262 |
| direct product | C2×D1131 |
| unambiguous semidirect product | (C2×C3)⋊D377 |
| unambiguous semidirect product | (C2×C13)⋊D87 |
| unambiguous semidirect product | (C2×C29)⋊D39 |
| Fitting, socle | C2×C3×C13×C29 ⋊ C2 |
| derived, Hall | C3×C13×C29 ⋊ C22 |
| Hall | C13×C29 ⋊ C2×D3 |
| Hall | C3×C29 ⋊ C2×D13 |
| Hall | C3×C13 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D39 |
| Sylow | C13 ⋊ C2×D87 |
| Sylow | C3 ⋊ C2×D377 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1131 |
| commutator, cosocle, hypocenter | C3×C13×C29 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C29 | C2 |
| LCS | G ▷ C3×C13×C29 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2262 |
1134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3393, C2×C3⋊(C29⋊(D13⋊C3)), D3×D1131, … |
| maximal normal subgroup of | C2×C3⋊(C29⋊(D13⋊C3)), C2×C3×D1131, C2×C5×D1131, … |
| maximal quotient of | C2×D3393, D3×D1131, C2×C3⋊D1131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4524, 52);