Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C222 |
| direct product | C22×#6431743 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×#127 |
| commutator, Frattini, cosocle | C22×C4 | C27 |
| socle | C23 | C22×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×#41 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
1013144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72303140, C2×#72239654 |
| maximal normal subgroup of | #72303140, C2×#72239654 |
Past the SmallGroups library coverage — no SmallGroups id.