Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C43 · Schur multiplier (H2) = C24 |
| direct product | C43×#19137 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C43 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C43 |
| socle | C22×C43 | C2×#121 |
| prime radical | C22×D4×C43 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C43 ◁ C2×C42×C43 ◁ G | |
662 conjugacy classes of subgroups.
1978 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 12125);