Finite Group DatabasebetaFinite Group Databasebeta| order | 4192 |
| isoclinism | isoclinic class of D131 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×D131 |
| Fitting | C42×C131 ⋊ C2 |
| derived, Sylow | C131 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D131 |
| commutator, hypocenter | C131 | C2×C42 |
| Frattini | C22 | C22×D131 |
| Fitting | C42×C131 | C2 |
| socle, cosocle | C22×C131 | C23 |
| prime radical | C22×D131 | C22 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C42 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2096 |
1072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4192, 94);