Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11549 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C43 · Schur multiplier (H2) = C22×C4 |
| direct product | C43×#13228 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C43 | C2×#99 |
| commutator | C22×C4 | C22×C4×C43 |
| Frattini, cosocle | C22×Q8 | C23×C43 |
| prime radical | C22×D4×C43 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C2×C4×Q8×C43 ◁ G | |
490 conjugacy classes of subgroups.
1591 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 6216);