Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C2×D4×#2397 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C4 | C25 |
| commutator, Frattini, cosocle | C24 | C27 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
450344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72280587 |
| maximal normal subgroup of | C2×#72280587 |
| automorphism group of | #7163 |
Past the SmallGroups library coverage — no SmallGroups id.