Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| isoclinism | isoclinic class of Dic82 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×C22⋊D41 |
| Fitting | C24×C41 ⋊ C2 |
| Sylow | C41 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D41 |
| commutator, cosocle | C2×C41 | C24 |
| Frattini | C2 | C23×D41 |
| Fitting | C24×C41 | C2 |
| socle | C23×C41 | C22 |
| hypercenter | C24 | D41 |
| hypocenter | C41 | C22×D4 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C23 ◁ C24 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14580212, #14580213, #14580215, … |
| maximal normal subgroup of | #14580212, #14580213, #14580215, … |
| maximal quotient of | C22×#10620281, C22×C22⋊Dic41, C22×#10620279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 183);