Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C212 |
| direct product | C2×#72215536 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#1790 |
| commutator | C22×D4 | C24×C4 |
| Frattini, cosocle | C22×#41 | C25 |
| prime radical | C22×#52004 | C2 |
| LCS | G ▷ C22×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C24×C4 ◁ C24×#41 ◁ G | |
| LECS | G ▷ C22×#41 ▷ C23 ▷ C2 ▷ C1 | |
77230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | #72250575, C2×#72216977, C2×#72216528, … |
| maximal normal subgroup of | #72250575, C2×#72216977, C2×#72216528, … |
Past the SmallGroups library coverage — no SmallGroups id.