Finite Group DatabasebetaFinite Group Databasebeta| order | 12052 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×Dic131 |
| unambiguous semidirect product | C131⋊(C4×C23) |
| derived, Sylow | C131 ⋊ C4×C23 |
| Hall | C23×C131 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D131 |
| commutator, hypocenter | C131 | C4×C23 |
| Frattini | C2 | C23×D131 |
| Fitting, socle, prime radical | C2×C23×C131 | C2 |
| cosocle | C2×C131 | C2×C23 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C2×C23 | |
12 conjugacy classes of subgroups.
3082 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×Dic131, C23×Dic393 |
| maximal normal subgroup of | C3×C23×Dic131 |
| maximal quotient of | C3×C23×Dic131, C23×Dic393 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12052, 3);