Finite Group DatabasebetaFinite Group Databasebeta| order | 10700 |
| isoclinism | isoclinic class of D107 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D107 |
| unambiguous semidirect product | C107⋊(C22×C52) |
| unambiguous semidirect product | (C2×C107)⋊(C2×C52) |
| Fitting, socle | C2×C52×C107 ⋊ C2 |
| derived, Sylow | C107 ⋊ C22×C52 |
| Hall | C52×C107 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D107 |
| commutator, cosocle, hypocenter | C107 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C107 | C2 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C2×C52 | |
80 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C52⋊C3×D107, C52×D3×D107, C2×C3×C52×D107, … |
| maximal normal subgroup of | C2×C52⋊C3×D107, C2×C3×C52×D107 |
| maximal quotient of | C52×D3×D107, C2×C3×C52×D107, C2×C52×D321 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10700, 36);