Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C2×#72231551 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×#442 |
| commutator | C2×C8 | C25×C4 |
| Frattini, cosocle | C22×C8 | C26 |
| prime radical | C2×#7622820 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×#41 ◁ C22×#2875 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
74204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72343913 |
| maximal normal subgroup of | #72343913 |
| maximal quotient of | C2×#72257081, #72317461, #72322017 |
Past the SmallGroups library coverage — no SmallGroups id.