Finite Group DatabasebetaFinite Group Databasebeta| order | 18105 |
| isoclinism | isoclinic class of C71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C3×C17×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C3×C5×C17 |
| Hall | C17×C71 ⋊ C3×C5 |
| Hall | C3×C71 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | C71⋊C5 |
| commutator, cosocle, hypocenter | C71 | C3×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C3×C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3621 |
969 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C17×C71⋊C5, C3×C17×D71⋊C5, C3×D17×C71⋊C5, … |
| maximal normal subgroup of | C2×C3×C17×C71⋊C5, C3×C17×D71⋊C5, C3×D17×C71⋊C5, … |
| maximal quotient of | C2×C3×C17×C71⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18105, 2);