Finite Group DatabasebetaFinite Group Databasebeta| order | 23870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D7×ΓL(1,𝔽32) |
| unambiguous semidirect product | C7⋊(C2×C11×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (D7×C31)⋊(C5×C11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D7×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C7×C31 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C31 | C2×C5 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C11 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2387 |
605 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23870, 41);