Finite Group Databasebeta

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C3×D55⋊D39 #38788219

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

Aliases

direct productC3×D55⋊D39
unambiguous semidirect productD55⋊(C3×D39)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derivedC3×C5×C11×C13 ⋊ C22×C3
HallC32×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×C3×D3
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C3×D3×D5
HallC32×C13 ⋊ D5×D11
HallC32×C11 ⋊ D5×D13
HallC5×C13 ⋊ C3×D3×D11
HallC5×C11 ⋊ C2×C3×D39
HallC32×C5 ⋊ D11×D13
SylowC13 ⋊ C3×D15⋊D11
SylowC11 ⋊ C3×D5×D39
SylowC32 ⋊ D55⋊D13
SylowC5 ⋊ C3×D11×D39

Subgroups

subgroupG/H
center, hypercenterC3D55⋊D39
commutator, cosocle, hypocenterC3×C5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C3×C5×C11×C13
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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

1737 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 450);