Finite Group DatabasebetaFinite Group Databasebeta| order | 4096 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#72225096 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72225095 |
| commutator | C2×C16 | C23×C42 |
| Frattini, cosocle | C2×#346 | C25 |
| prime radical | C2×#7623252 | C22 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C2×C4×#131 ◁ C2×#479908 ◁ G | |
| LECS | G ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
12805 conjugacy classes of subgroups.
| transitive degree | μt(G) = 128 |
274 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#72225134 |
| maximal normal subgroup of | C2×#72225134 |
Past the SmallGroups library coverage — no SmallGroups id.