Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C226 |
| direct product | C2×#72236479 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C4 | C26 |
| commutator, Frattini, cosocle | C23 | C28 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
At least 6712 conjugacy classes of subgroups; only the 451400 normal subgroups are shown.
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72310675 |
| maximal normal subgroup of | C2×#72310675 |
| automorphism group of | #12014, #12614, #12615, … |
Past the SmallGroups library coverage — no SmallGroups id.