Finite Group DatabasebetaFinite Group Databasebeta| order | 18798 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C241⋊C3)⋊D13 |
| Fitting, socle, derived, Hall | C13×C241 ⋊ C2×C3 |
| Hall | C13×C241⋊C3 ⋊ C2 |
| Hall | D3133 ⋊ C3 |
| Hall | C241⋊C3 ⋊ D13 |
| Sylow | C241 ⋊ C3×D13 |
| Sylow | C13 ⋊ D241⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C241 | C2×C3 |
| LCS | G ▷ C13×C241 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3133 |
Polycyclic presentation:
2,3,13,241|c^a=c^12,d^a=d^240,d^b=d^15544 conjugacy classes — view the full character table.
| maximal subgroup of | #49178112, #49178113, D13×D241⋊C3, … |
| maximal normal subgroup of | #49178112, #49178113, D13×D241⋊C3, … |
| maximal quotient of | #49178088, C2×(C241⋊C3)⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18798, 21);