Finite Group DatabasebetaFinite Group Databasebeta| order | 20748 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#23780550 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #23780550 |
| commutator, cosocle, hypocenter | C7×C13×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13×C19 | C2×C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3458 |
678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20748, 331);