Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C28 · Schur multiplier (H2) = C227 |
| direct product | C24×#3109 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C28 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26 ◁ C25×C42 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Only the 457064 normal subgroups are shown; non-normal subgroups are omitted.
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72305173, C2×#72311718, #72314597 |
| maximal normal subgroup of | #72305173, C2×#72311718, #72314597 |
| automorphism group of | #12650, #12677, #12943, … |
Past the SmallGroups library coverage — no SmallGroups id.