Finite Group Databasebeta

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D5×C3⋊(C11⋊(D13⋊C3)) #38788103

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

Aliases

direct productD5×C3⋊(C11⋊(D13⋊C3))
unambiguous semidirect product(C3×D5)⋊(C11⋊(D13⋊C3))
unambiguous semidirect product(D5×C11)⋊(C3⋊(D13⋊C3))
unambiguous semidirect product(D5×C13⋊C3)⋊D33
unambiguous semidirect product(D5×D429)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C13 ⋊ C22×C3
HallC3×C5×C11×C13⋊C3 ⋊ C22
HallC3×C11×C13⋊C3 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×C3×D3
HallC3×C5×C13⋊C3 ⋊ C2×D11
HallC11×C13 ⋊ C3×D3×D5
HallC3×C13⋊C3 ⋊ D5×D11
HallC5×C13 ⋊ C2×C3×D33
HallC5×C11 ⋊ C2×C3⋊(D13⋊C3)
SylowC13 ⋊ C3×D5×D33
SylowC11 ⋊ D5×C3⋊(D13⋊C3)
SylowC5 ⋊ C2×C3⋊(C11⋊(D13⋊C3))

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C13C22×C3
LCSG ▷ C3×C5×C11×C13
UCSC1

176 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 2145

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 334);