Finite Group Databasebeta

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C7×#10587716⋊D5 #50303994

order38220
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×#10587716⋊D5
unambiguous semidirect product#10587716⋊(C7×D5)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C22×C3
derivedC5×C7×C13 ⋊ C22×C3×C7
HallC7×D13×D35 ⋊ C3
HallC5×C7×#63270 ⋊ C22
HallC7×#63270 ⋊ C2×D5
HallC72×C13 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×C7×AGL(1,𝔽7)
SylowC72 ⋊ D5×D13⋊C3
SylowC13 ⋊ C2×C7×C5⋊AGL(1,𝔽7)
SylowC5 ⋊ C7×#10587716⋊C2

Subgroups

subgroupG/H
center, hypercenterC7#10587716⋊D5
commutator, cosocle, hypocenterC5×C7×C13C22×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

168 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 2730

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 680);