Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C2×#72234840 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C23×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C27 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×D4 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
Only the 38712 normal subgroups are shown; non-normal subgroups are omitted.
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72256706 |
| maximal normal subgroup of | #72256706 |
| maximal quotient of | #72342352 |
| automorphism group of | #12633, #12719 |
Past the SmallGroups library coverage — no SmallGroups id.