Finite Group DatabasebetaFinite Group Databasebeta| order | 8192 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3298534883328 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C43×C82×C16 |
| abelian | C4×C8×C162 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4×C82 | C24 |
| socle, prime radical | C24 | C2×C4×C82 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C2×C4×C82 ▷ C2×C42 ▷ C22 ▷ C1 | |
44558 conjugacy classes of subgroups.
8192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×C16×C32, C4×C163, C82×C162, … |
| maximal normal subgroup of | C4×C8×C16×C32, C4×C163, C82×C162, … |
| maximal quotient of | C4×C8×C16×C32, C4×C163, C82×C162, … |
Past the SmallGroups library coverage — no SmallGroups id.