Finite Group DatabasebetaFinite Group Databasebeta| order | 10633 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×7−1+2 |
| unambiguous semidirect product | C49⋊(C7×C31) |
| unambiguous semidirect product | (C31×C49)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C7×C31 | C72 |
| commutator, Frattini, cosocle | C7 | C72×C31 |
| prime radical | C72×C31 | C7 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C7×C31 ◁ G | |
24 conjugacy classes of subgroups.
1705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10633, 4);