Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#72215653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #8534 |
| commutator | C22×C22⋊C4 | C23×C4 |
| Frattini, cosocle | C22×#120 | C24 |
| prime radical | C2×#648360 | C2 |
| LCS | G ▷ C22×C22⋊C4 ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C23×#120 ◁ G | |
| LECS | G ▷ C22×#120 ▷ C24 ▷ C22 ▷ C1 | |
106048 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72215688, #72267468, C2×#72216504, … |
| maximal normal subgroup of | C2×#72215688, #72267468, C2×#72216504, … |
Past the SmallGroups library coverage — no SmallGroups id.