Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #31076 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C43 · Schur multiplier (H2) = C22×C4 |
| direct product | C43×#32704 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C43 | H(3,𝔽4) |
| commutator, Frattini, cosocle | C22×C4 | C24×C43 |
| socle | C2×C43 | #2804 |
| prime radical | C43×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C43 ◁ C22×C4×C43 ◁ G | |
556 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 25692);