Finite Group Databasebeta

← Prev (#38788189) Next (#38788191) →

C3×C11×C13×ΓL(1,𝔽16) #38788190

order25740
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C13×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C3×C11×C13×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derivedC3×C5 ⋊ C3×C4×C11×C13
HallC32×C11×C13 ⋊ AGL(1,𝔽5)
HallC5×C11×C13 ⋊ C3×Dic3
HallC32×C5×C13 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C13
HallC32×C13 ⋊ C11×AGL(1,𝔽5)
HallC32×C11 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×C11×Dic3
HallC5×C11 ⋊ C3×Dic3×C13
HallC32×C5 ⋊ C4×C11×C13
SylowC32 ⋊ C11×C13×AGL(1,𝔽5)
SylowC5 ⋊ C3×C11×Dic3×C13

Subgroups

subgroupG/H
center, hypercenterC3×C11×C13ΓL(1,𝔽16)
commutator, hypocenterC3×C5C3×C4×C11×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×D5×C11×C13C2
cosocleC3×D5C2×C3×C11×C13
LCSG ▷ C3×C5
UCSC1 ◁ C3×C11×C13

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) = 4290

Conjugacy classes & character table

3861 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 421);