Finite Group DatabasebetaFinite Group Databasebeta| order | 12028 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C97 · Schur multiplier (H2) = C2 |
| direct product | C2×D31×C97 |
| unambiguous semidirect product | C31⋊(C22×C97) |
| unambiguous semidirect product | (C2×C31)⋊(C2×C97) |
| Fitting, socle | C2×C31×C97 ⋊ C2 |
| derived, Sylow | C31 ⋊ C22×C97 |
| Hall | C31×C97 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C97 | D31 |
| commutator, cosocle, hypocenter | C31 | C22×C97 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C97 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C97 | |
20 conjugacy classes of subgroups.
3298 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C97×D31⋊C3, C2×#31825225, C2×#31825224, … |
| maximal normal subgroup of | C2×C97×D31⋊C3, C2×#31825225, C2×#31825224, … |
| maximal quotient of | D3×D31×C97, C2×C3×D31×C97, C2×C97×D93 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12028, 10);