Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C211 · Schur multiplier (H2) = C254 |
| direct product | C22×#72258201 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C4 | C28 |
| commutator, Frattini, cosocle | C2 | C211 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ G | |
| LECS | G ▷ C2 ▷ C1 | |
8935877595 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×H(11,𝔽2), C2×#72274291, C22×2−1+10 |
| maximal normal subgroup of | C22×H(11,𝔽2), C2×#72274291, C22×2−1+10 |
Past the SmallGroups library coverage — no SmallGroups id.