Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#10620270 |
| derived, Sylow | C41 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #4223 |
| commutator, hypocenter | C41 | C2×C16 |
| Frattini | C4 | C2×#4223 |
| Fitting | C2×C4×C41 | C4 |
| socle, prime radical | C22×C41 | C8 |
| cosocle | #66491 | C22 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1312 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10620270, #14581222, #14581224, … |
| maximal normal subgroup of | C4×#10620270, #14581222, #14581224, … |
| maximal quotient of | C4×#10620270, C22⋊#10620270, C4⋊#10620270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 218);