Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C2×#72216464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #32898 |
| commutator, Frattini, cosocle | C22×C22⋊C4 | C25 |
| LCS | G ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C25 ◁ C23×#120 ◁ G | |
| LECS | G ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
61794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | #72284919, C2×#72216737, C2×#72340869 |
| maximal normal subgroup of | #72284919, C2×#72216737 |
| maximal quotient of | C2×#72216466 |
Past the SmallGroups library coverage — no SmallGroups id.