Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42 |
| direct product | C2×#72213016 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42 | C2×#127 |
| commutator | C42 | C23×C42 |
| Frattini, cosocle | C22×C42 | C25 |
| socle | C23 | C4×#390 |
| prime radical | C2×#60673 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42 ◁ C23×C4×C8 ◁ G | |
| LECS | G ▷ C22×C42 ▷ C22 ▷ C1 | |
16592 conjugacy classes of subgroups.
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72213062 |
| maximal normal subgroup of | C2×#72213062, #72216307, C2×#72216677 |
Past the SmallGroups library coverage — no SmallGroups id.