Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C210 · Schur multiplier (H2) = C244 |
| direct product | C2×#72258201 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C4 | C28 |
| commutator, Frattini, cosocle | C2 | C210 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ G | |
| LECS | G ▷ C2 ▷ C1 | |
229944818 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
1028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×2−1+10, #72274291, C2×H(11,𝔽2), … |
| maximal normal subgroup of | C2×2−1+10, #72274291, C2×H(11,𝔽2), … |
| maximal quotient of | C22×#72258201 |
Past the SmallGroups library coverage — no SmallGroups id.