Finite Group DatabasebetaFinite Group Databasebeta| order | 12028 |
| isoclinism | isoclinic class of #87604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#87604 |
| Fitting, socle, Hall | C31×C97 ⋊ C4 |
| derived, Sylow | C97 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #87604 |
| commutator, hypocenter | C97 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C97 | C4 |
| prime radical | C31×D97 | C2 |
| cosocle | D97 | C2×C31 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C31 | |
12 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#87604⋊C3, #49115335, #49115336, … |
| maximal normal subgroup of | C31×#87604⋊C3, #49115335, #49115336, … |
| maximal quotient of | C3×C31×#87604, C31×C3⋊#87604 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12028, 6);