Finite Group DatabasebetaFinite Group Databasebeta| order | 18755 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C31 · Schur multiplier (H2) = C11 |
| direct product | C31×#10597245 |
| Fitting, socle, Hall | C112×C31 ⋊ C5 |
| derived, Sylow | C112 ⋊ C5×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #10597245 |
| commutator, cosocle, hypocenter | C112 | C5×C31 |
| Frattini | C1 | G |
| Fitting, socle | C112×C31 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C31 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1705 |
899 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18755, 26);