Finite Group DatabasebetaFinite Group Databasebeta| order | 10700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D25×D107 |
| unambiguous semidirect product | (D25×C107)⋊C2 |
| unambiguous semidirect product | (C25×D107)⋊C2 |
| unambiguous semidirect product | D2675⋊C2 |
| Fitting, derived, Hall | C25×C107 ⋊ C22 |
| Sylow | C107 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C25×C107 | C22 |
| Frattini | C5 | D5×D107 |
| socle | C5×C107 | C2×D5 |
| LCS | G ▷ C25×C107 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D25×D107, D75×D107, D25×D321, … |
| maximal normal subgroup of | C3×D25×D107 |
| maximal quotient of | C3×D25×D107, D75×D107, D25×D321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10700, 8);