Finite Group DatabasebetaFinite Group Databasebeta| order | 15855 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#15691748 |
| Fitting, socle, Hall | C5×C7×C151 ⋊ C3 |
| derived, Hall | C7×C151 ⋊ C3×C5 |
| Hall | C5×C151 ⋊ ΓL(1,𝔽8) |
| Sylow | C151 ⋊ C5×ΓL(1,𝔽8) |
| Hall | C5×C7 ⋊ C151⋊C3 |
| Sylow | C7 ⋊ C5×C151⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #15691748 |
| commutator, cosocle, hypocenter | C7×C151 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C151 | C3 |
| LCS | G ▷ C7×C151 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5285 |
1775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×#15691748, C5×#20263623, C5×#20263627, … |
| maximal normal subgroup of | C2×C5×#15691748, C5×#20263623, C5×#20263627, … |
| maximal quotient of | C2×C5×#15691748 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15855, 5);