Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #468 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C43 · Schur multiplier (H2) = C28 |
| direct product | C22×C43×#501 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C43 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C43 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C43 ◁ C22×C42×C43 ◁ G | |
2142 conjugacy classes of subgroups.
2752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 53644);