Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#72213781 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #142536 |
| commutator, Frattini, cosocle | #2309 | C24 |
| LCS | G ▷ #2309 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C24×C4 ◁ C2×#2309 ◁ G | |
| LECS | G ▷ #2309 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
13452 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | #72340454 |
| maximal normal subgroup of | #72340454 |
Past the SmallGroups library coverage — no SmallGroups id.