Finite Group DatabasebetaFinite Group Databasebeta| order | 18354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D437 |
| unambiguous semidirect product | C23⋊(ΓL(1,𝔽8)⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C19×C23 | C2×C3 |
| LCS | G ▷ C7×C19×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3059 |
Polycyclic presentation:
2,3,7,19,23|c^a=c^6,d^a=d^18,e^a=e^22,c^b=c^21097 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18354, 46);