Finite Group DatabasebetaFinite Group Databasebeta| order | 12028 |
| isoclinism | isoclinic class of D97 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C31×D97 |
| unambiguous semidirect product | C97⋊(C22×C31) |
| unambiguous semidirect product | (C2×C97)⋊(C2×C31) |
| Fitting, socle | C2×C31×C97 ⋊ C2 |
| derived, Sylow | C97 ⋊ C22×C31 |
| Hall | C31×C97 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D97 |
| commutator, cosocle, hypocenter | C97 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C97 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C31 | |
20 conjugacy classes of subgroups.
3100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C31×D97⋊C3, C2×#31825221, C2×#31825220, … |
| maximal normal subgroup of | C2×C31×D97⋊C3, C2×#31825221, C2×#31825220, … |
| maximal quotient of | D3×C31×D97, C2×C3×C31×D97, C2×C31×D291 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12028, 11);