Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#4223 |
| unambiguous semidirect product | D41⋊C42 |
| Fitting | C2×C4×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #4223 |
| commutator, hypocenter | C41 | C2×C42 |
| Frattini | C2 | C22×#4223 |
| Fitting | C2×C4×C41 | C4 |
| socle | C22×C41 | C2×C4 |
| prime radical | C22×D41 | C22 |
| cosocle | C2×D41 | C23 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #14581201, #14581206, #14581208, … |
| maximal normal subgroup of | #14581201, #14581206, #14581208, … |
| maximal quotient of | C42×#4223, C2×(C2×#4223)⋊C4, #14581272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 222);