Finite Group Databasebeta

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D13×C3⋊(C5⋊(C7⋊D7)) #50304446

order38220
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C7

Aliases

direct productD13×C3⋊(C5⋊(C7⋊D7))
unambiguous semidirect product(C3×D13)⋊(C5⋊(C7⋊D7))
unambiguous semidirect product(C5×D13)⋊(C3⋊(C7⋊D7))
unambiguous semidirect product(C7×D13)⋊D105

Splittings

Fitting, socle, derived, HallC3×C5×C72×C13 ⋊ C22
HallC5×C72×C13 ⋊ C2×D3
HallC3×C72×C13 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D13
HallC72×C13 ⋊ C2×D15
HallC5×C72 ⋊ D3×D13
HallC3×C5×C13 ⋊ C2×C7⋊D7
HallC3×C72 ⋊ D5×D13
HallC5×C13 ⋊ C2×C3⋊(C7⋊D7)
SylowC72 ⋊ D13×D15
HallC3×C13 ⋊ C2×C5⋊(C7⋊D7)
HallC3×C5 ⋊ D13×C7⋊D7
SylowC13 ⋊ C2×C3⋊(C5⋊(C7⋊D7))
SylowC5 ⋊ D13×C3⋊(C7⋊D7)
SylowC3 ⋊ D13×C5⋊(C7⋊D7)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72×C13
UCSC1

400 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 124 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) = 9555

Conjugacy classes & character table

2952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1132);