Finite Group DatabasebetaFinite Group Databasebeta| order | 18746 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C103 · Schur multiplier (H2) = C1 |
| direct product | C13×D7×C103 |
| unambiguous semidirect product | C7⋊(C2×C13×C103) |
| Fitting, socle, Hall | C7×C13×C103 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C13×C103 |
| Hall | C7×C103 ⋊ C2×C13 |
| Hall | C7×C13 ⋊ C2×C103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C103 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C13×C103 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C103 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C13×C103 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9373 |
6695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D7×D103, D7×D13×C103, D7×D1339, … |
| maximal normal subgroup of | C13×D7×D103, D7×D13×C103, D7×D1339, … |
| maximal quotient of | C13×Dic7×C103, C2×C13×D7×C103 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18746, 5);