Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C213 |
| direct product | C4×#245225 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #2403 |
| commutator | C25 | C24×C4 |
| Frattini, cosocle | C26 | C25 |
| socle | C23 | C2×#2403 |
| prime radical | C2×#245225 | C2 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C26 ▷ C22 ▷ C1 | |
61336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#72209653, C2×C4×#245225 |
| maximal normal subgroup of | C2×C4×#245225 |
| maximal quotient of | C4×B(5,𝔽2), #72342880, C2×C4×#245225 |
Past the SmallGroups library coverage — no SmallGroups id.