Finite Group DatabasebetaFinite Group Databasebeta| order | 2048 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C214 |
| direct product | C2×#72216432 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24 | #2846 |
| commutator, Frattini, cosocle | C26 | C25 |
| LCS | G ▷ C26 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ C27 ◁ G | |
| LECS | G ▷ C26 ▷ C23 ▷ C1 | |
132440 conjugacy classes of subgroups; only the 1120 normal subgroups are shown.
This group has 132440 conjugacy classes of subgroups — too many to draw. Only its 1120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
158 conjugacy classes — view the full character table.
| maximal subgroup of | #72334272, #72334284, C2×#72216737, … |
| maximal normal subgroup of | #72334272, #72334284, C2×#72216737, … |
| maximal quotient of | C2×#72216433 |
Past the SmallGroups library coverage — no SmallGroups id.