Finite Group DatabasebetaFinite Group Databasebeta| order | 10052 |
| automorphism | Aut(G) order 10795848 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5026 |
| direct product | C2×D2513 |
| unambiguous semidirect product | (C2×C7)⋊D359 |
| unambiguous semidirect product | (C2×C359)⋊D7 |
| Fitting, socle | C2×C7×C359 ⋊ C2 |
| derived, Hall | C7×C359 ⋊ C22 |
| Sylow | C359 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D359 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2513 |
| commutator, cosocle, hypocenter | C7×C359 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C359 | C2 |
| LCS | G ▷ C7×C359 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)⋊D359, D3×D2513, C2×C3×D2513, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)⋊D359, C2×C3×D2513, D10052 |
| maximal quotient of | D3×D2513, C2×C3×D2513, C2×D7539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10052, 7);