Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
| direct product | C2×#144378 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #10336 |
| commutator, Frattini, cosocle | C23×D4 | C24 |
| LCS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C24×D4 ◁ G | |
| LECS | G ▷ C23×D4 ▷ C23 ▷ C2 ▷ C1 | |
10813 conjugacy classes of subgroups.
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72209844, C2×B(5,𝔽2), #72225612, … |
| maximal normal subgroup of | C2×#72209844, C2×B(5,𝔽2), #72218868, … |
| maximal quotient of | C2×#72210565, #72218868, D3×#144378, … |
Past the SmallGroups library coverage — no SmallGroups id.