Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C213 |
| direct product | C2×C3×#245225 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | #2403 |
| commutator, Frattini, cosocle | C25 | C25×C3 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ C26×C3 ◁ G | |
62830 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#72209653 |
| maximal quotient of | C2×C3×B(5,𝔽2) |
Past the SmallGroups library coverage — no SmallGroups id.