Finite Group DatabasebetaFinite Group Databasebeta| order | 8192 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C278 |
| abelian | C213 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
37558989808526 conjugacy classes of subgroups.
8192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C212×C4, C214, C213×C3, … |
| maximal normal subgroup of | C212×C4, C214, C213×C3, … |
| maximal quotient of | C212×C4, C214, C213×C3, … |
| automorphism group of | #21109, #21110, #21111, … |
Past the SmallGroups library coverage — no SmallGroups id.