Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1402 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C89 · Schur multiplier (H2) = C2 |
| direct product | C89×#1403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C2×C4×C89 |
| Frattini, cosocle | #124 | C22×C89 |
| prime radical | H(5,𝔽2)×C89 | C4 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C22×C89 ◁ C2×C4×C89 ◁ #124×C89 ◁ G | |
112 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 135);