Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C2×#394038 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#392 |
| commutator, Frattini, cosocle | C23×C4 | C25 |
| LCS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
39095 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214896, #72302585, #72302771 |
| maximal normal subgroup of | C2×#72214896, #72302585, #72302771 |
| maximal quotient of | C2×#72213902, C2×#72214464, C2×#72239575, … |
Past the SmallGroups library coverage — no SmallGroups id.