Finite Group DatabasebetaFinite Group Databasebeta| order | 18411 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#11762245 |
| Fitting, socle, Hall | C17×C192 ⋊ C3 |
| derived, Sylow | C192 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #11762245 |
| commutator, cosocle, hypocenter | C192 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C192 | C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C17 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6137 |
2091 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×#14524206, C17×#14524208, D17×#11762245, … |
| maximal normal subgroup of | C17×#14524206, C17×#14524208, D17×#11762245, … |
| maximal quotient of | C2×C17×#11762245 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18411, 4);