Finite Group DatabasebetaFinite Group Databasebeta| order | 15855 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15691749⋊C5 |
| Fitting, socle, derived, Hall | C7×C151 ⋊ C3×C5 |
| Hall | C7×C151⋊C5 ⋊ C3 |
| Hall | #15691749 ⋊ C5 |
| Hall | C151⋊C5 ⋊ ΓL(1,𝔽8) |
| Sylow | C151 ⋊ C5×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C151⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C151 | C3×C5 |
| LCS | G ▷ C7×C151 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1057 |
Polycyclic presentation:
3,5,7,151|c^a=c^2,d^a=d^118,d^b=d^5995 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#15691749⋊C5, #20263624⋊C5, #20263628⋊C5, … |
| maximal normal subgroup of | C2×#15691749⋊C5, #20263624⋊C5, #20263628⋊C5, … |
| maximal quotient of | C2×#15691749⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15855, 10);