Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C212 |
| direct product | C2×#72213827 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #23900 |
| 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 | |
120798 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72215688, C2×#72216969, C22×#72213827, … |
| maximal normal subgroup of | C2×#72215688, C22×#72213827, #72292097, … |
| maximal quotient of | C22×#72213827, #72292129, #72340449, … |
Past the SmallGroups library coverage — no SmallGroups id.