Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D41 |
| Fitting | M16×C41 ⋊ C2 |
| Sylow | C41 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D41 |
| commutator, socle | C2×C41 | C22×C4 |
| Fitting | M16×C41 | C2 |
| prime radical | C22×D41 | C4 |
| cosocle | C4×C41 | C23 |
| hypercenter | M16 | D41 |
| hypocenter | C41 | C2×M16 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C4 ◁ M16 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #100×D41, #101×D41, #14580317, … |
| maximal normal subgroup of | #100×D41, #101×D41, #14580317, … |
| maximal quotient of | #97×D41, M16×Dic41, #14580288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 149);