Finite Group DatabasebetaFinite Group Databasebeta| order | 2292 |
| isoclinism | isoclinic class of D191 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic191 |
| unambiguous semidirect product | C191⋊(C3×C4) |
| derived, Sylow | C191 ⋊ C3×C4 |
| Hall | C3×C191 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D191 |
| commutator, hypocenter | C191 | C3×C4 |
| Frattini | C2 | C3×D191 |
| Fitting, socle, prime radical | C2×C3×C191 | C2 |
| cosocle | C2×C191 | C2×C3 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 198 |
| transitive degree | μt(G) = 2292 |
582 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic191, C3×Dic955, C3×Dic191⋊C5, … |
| maximal normal subgroup of | C3×C5×Dic191, C3×Dic191⋊C5, C3×C7×Dic191, … |
| maximal quotient of | C3×C5×Dic191, C3×Dic955, C3×C191⋊AGL(1,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2292, 3);