Finite Group DatabasebetaFinite Group Databasebeta| order | 20370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C97 · Schur multiplier (H2) = C1 |
| direct product | D5×ΓL(1,𝔽8)×C97 |
| unambiguous semidirect product | C5⋊(C2×ΓL(1,𝔽8)×C97) |
| unambiguous semidirect product | (C7×D5)⋊(C3×C97) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D5×ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C5×C7 | C2×C3×C97 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C97 | C2×C3 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C97 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3395 |
1940 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20370, 34);