Finite Group DatabasebetaFinite Group Databasebeta| order | 16275 |
| isoclinism | isoclinic class of ΓL(1,𝔽32) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52×C7 · Schur multiplier (H2) = C5 |
| Fitting, socle | C3×C5×C7×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C3×C52×C7 |
| Hall | C3×C7×C31 ⋊ C52 |
| Hall | C7×C31 ⋊ C3×C52 |
| Hall | C3×C31 ⋊ C52×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C7 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C3×C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C5×C7 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3255 |
1155 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C7×D31⋊C5, C3×C5×C7⋊(D31⋊C5), C3×C5×D7×ΓL(1,𝔽32), … |
| maximal normal subgroup of | C3×C5×C7×D31⋊C5, C3×C5×C7⋊(D31⋊C5), C3×C5×D7×ΓL(1,𝔽32), … |
| maximal quotient of | C2×C3×C5×C7×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16275, 16);