Finite Group DatabasebetaFinite Group Databasebeta| order | 11421 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6909 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C47 · Schur multiplier (H2) = C34 |
| direct product | C47×#6911 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C47 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C33×C47 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C47 ◁ C33×C47 ◁ G | |
160 conjugacy classes of subgroups.
1645 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11421, 58);