Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C213 |
| direct product | C2×#72214565 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #32898 |
| commutator, Frattini, cosocle | C22×#41 | C25 |
| LCS | G ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C4 ◁ C23×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1 | |
At least 7789 conjugacy classes of subgroups; only the 1728 normal subgroups are shown.
158 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72214565 |
| maximal quotient of | C2×#72214572, D3×#72214565 |
Past the SmallGroups library coverage — no SmallGroups id.