Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#4223 |
| unambiguous semidirect product | D41⋊(C22×C4) |
| Fitting, socle | C23×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #4223 |
| commutator, hypocenter | C41 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C41 | C4 |
| prime radical | C23×D41 | C2 |
| cosocle | D41 | C24 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#4223)⋊C4, C22⋊C4×#4223, #14581283, … |
| maximal normal subgroup of | C2×(C2×#4223)⋊C4, C22⋊C4×#4223, #14581283, … |
| maximal quotient of | C22×C4×#4223, C22×C22⋊#4223, C22×C4⋊#4223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 235);