Finite Group DatabasebetaFinite Group Databasebeta| order | 10700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D107 |
| unambiguous semidirect product | (D5×C107)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D107)⋊(C2×C5) |
| unambiguous semidirect product | D535⋊(C2×C5) |
| Fitting, socle, Hall | C52×C107 ⋊ C22 |
| derived | C5×C107 ⋊ C22×C5 |
| Sylow | C107 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D107 |
| commutator, cosocle, hypocenter | C5×C107 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C107 | C22 |
| LCS | G ▷ C5×C107 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
1100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3874×D107, C3×C5×D5×D107, C5×D15×D107, … |
| maximal normal subgroup of | C3×C5×D5×D107 |
| maximal quotient of | C3×C5×D5×D107, C5×D15×D107, C5×D5×D321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10700, 21);