Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| automorphism | Aut(G) order 3660000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3050 |
| direct product | C2×D1525 |
| unambiguous semidirect product | (C2×C25)⋊D61 |
| unambiguous semidirect product | (C2×C61)⋊D25 |
| Fitting | C2×C25×C61 ⋊ C2 |
| derived, Hall | C25×C61 ⋊ C22 |
| Sylow | C61 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1525 |
| commutator, hypocenter | C25×C61 | C22 |
| Frattini | C5 | C2×D305 |
| Fitting | C2×C25×C61 | C2 |
| socle | C2×C5×C61 | D5 |
| LCS | G ▷ C25×C61 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
1528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25⋊(D61⋊C3), D3×D1525, C2×C3×D1525, … |
| maximal normal subgroup of | C2×C25⋊(D61⋊C3), C2×C3×D1525, D6100 |
| maximal quotient of | D3×D1525, C2×C3×D1525, C2×D4575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 20);