Finite Group DatabasebetaFinite Group Databasebeta| order | 10670 |
| isoclinism | isoclinic class of D97 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D97 |
| unambiguous semidirect product | C97⋊(C2×C5×C11) |
| Fitting, socle, Hall | C5×C11×C97 ⋊ C2 |
| derived, Sylow | C97 ⋊ C2×C5×C11 |
| Hall | C11×C97 ⋊ C2×C5 |
| Hall | C5×C97 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D97 |
| commutator, cosocle, hypocenter | C97 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C97 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C5×C11 | |
16 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×#87604, C5×C11⋊#87604, C5×D11×D97, … |
| maximal normal subgroup of | C5×C11×#87604, C5×C11⋊#87604, C5×D11×D97, … |
| maximal quotient of | C5×C11×Dic97, C2×C5×C11×D97, C3×C5×C11×D97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10670, 3);