Finite Group Databasebeta

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C5×C13×(C3⋊D3)⋊D11 #38788229

order25740
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC5×C13×(C3⋊D3)⋊D11
unambiguous semidirect product(C3⋊D3)⋊(C5×C13×D11)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derived, HallC32×C11 ⋊ C22×C5×C13
HallC32×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ D32
HallC32×C5×C13 ⋊ C2×D11
HallC32×C5×C11 ⋊ C22×C13
HallC11×C13 ⋊ C5×D32
HallC32×C13 ⋊ C2×C5×D11
HallC5×C11 ⋊ D32×C13
HallC32×C5 ⋊ C2×C13×D11
SylowC11 ⋊ C5×D32×C13
SylowC32 ⋊ C2×C5×C13×D11

Subgroups

subgroupG/H
center, hypercenterC5×C13(C3⋊D3)⋊D11
commutator, cosocle, hypocenterC32×C11C22×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32×C11
UCSC1 ◁ C5×C13

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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

2535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 460);