Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C216 |
| direct product | C2×#72213843 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#2846 |
| commutator, Frattini, cosocle | C23×C4 | C26 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C23×C42 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Only the 6568 normal subgroups are shown; non-normal subgroups are omitted.
212 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72215640 |
| maximal normal subgroup of | C2×#72215640 |
Past the SmallGroups library coverage — no SmallGroups id.