Finite Group Databasebeta

← Prev (#38788206) Next (#38788208) →

C3×D5×C11×D39 #38788207

order25740
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C11×D39
unambiguous semidirect product(C3×D5)⋊(C3×C11×D13)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derivedC3×C5×C13 ⋊ C22×C3×C11
HallC32×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×C3×D3
HallC32×C5×C13 ⋊ C22×C11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C3×D3×D5
HallC32×C13 ⋊ C2×D5×C11
HallC32×C11 ⋊ D5×D13
HallC5×C13 ⋊ C2×C3×D3×C11
HallC5×C11 ⋊ C2×C3×D39
HallC32×C5 ⋊ C2×C11×D13
SylowC13 ⋊ C3×D3×D5×C11
SylowC32 ⋊ D5×C11×D13
SylowC5 ⋊ C2×C3×C11×D39

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×D39
commutator, cosocle, hypocenterC3×C5×C13C22×C3×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C3×C11

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 438);