Finite Group Databasebeta

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C3×C11×C19×ΓL(1,𝔽16) #49178674

order37620
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C19×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C3×C11×C19×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C4
derivedC3×C5 ⋊ C3×C4×C11×C19
HallC32×C11×C19 ⋊ AGL(1,𝔽5)
HallC5×C11×C19 ⋊ C3×Dic3
HallC32×C5×C19 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C19
HallC32×C19 ⋊ C11×AGL(1,𝔽5)
HallC32×C11 ⋊ C19×AGL(1,𝔽5)
HallC5×C19 ⋊ C3×C11×Dic3
HallC5×C11 ⋊ C3×Dic3×C19
HallC32×C5 ⋊ C4×C11×C19
SylowC32 ⋊ C11×C19×AGL(1,𝔽5)
SylowC5 ⋊ C3×C11×Dic3×C19

Subgroups

subgroupG/H
center, hypercenterC3×C11×C19ΓL(1,𝔽16)
commutator, hypocenterC3×C5C3×C4×C11×C19
FrattiniC1G
Fitting, socleC32×C5×C11×C19C4
prime radicalC32×D5×C11×C19C2
cosocleC3×D5C2×C3×C11×C19
LCSG ▷ C3×C5
UCSC1 ◁ C3×C11×C19

112 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

5643 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 383);