Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic41 |
| Sylow | C41 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D41 |
| commutator | C2×C41 | C22×C4 |
| Fitting, prime radical | C2×D4×C41 | C2 |
| socle, cosocle | C22×C41 | C23 |
| hypercenter | C2×D4 | D41 |
| hypocenter | C41 | C4×D4 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14580416, D8×Dic41, SD16×Dic41, … |
| maximal normal subgroup of | #14580416, D8×Dic41, SD16×Dic41, … |
| maximal quotient of | C22⋊C4×Dic41, C4⋊C4×Dic41, #14580211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 109);