Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#72210482 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #131967 |
| commutator | C22×C22⋊C4 | C23×C4 |
| Frattini, cosocle | C2×#379 | C24 |
| prime radical | C2×#6499867 | C2 |
| LCS | G ▷ C22×C22⋊C4 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C26 ◁ C22×#2846 ◁ G | |
| LECS | G ▷ C2×#379 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
75610 conjugacy classes of subgroups.
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72216992, #72285069, #72292097, … |
| maximal normal subgroup of | C2×#72210568, #72285069, #72292097, … |
| maximal quotient of | #72285069, #72340453, #72340458 |
Past the SmallGroups library coverage — no SmallGroups id.