Finite Group DatabasebetaFinite Group Databasebeta| order | 18756 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D521 |
| unambiguous semidirect product | C521⋊(C22×C32) |
| unambiguous semidirect product | (C2×C521)⋊(C2×C32) |
| Fitting, socle | C2×C32×C521 ⋊ C2 |
| derived, Sylow | C521 ⋊ C22×C32 |
| Hall | C32×C521 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D521 |
| commutator, cosocle, hypocenter | C521 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C521 | C2 |
| LCS | G ▷ C521 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9378 |
4716 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18756, 36);