Finite Group Databasebeta

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D5×D13⋊#3862 #50304196

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

Aliases

direct productD5×D13⋊#3862
unambiguous semidirect productD13⋊(D5×#3862)
unambiguous semidirect product(D5×D13)⋊#3862

Splittings

Fitting, socle, derived, HallC5×C72×C13 ⋊ C22×C3
HallC72×D5×D13 ⋊ C3
HallC5×C13⋊#3862 ⋊ C22
HallC13⋊#3862 ⋊ C2×D5
HallC72×C13 ⋊ C2×C3×D5
HallD5×D13 ⋊ #3862
HallC5×C72 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C22×#3862
SylowC72 ⋊ D5×D13⋊C3
SylowC13 ⋊ C2×D5×#3862
SylowC5 ⋊ C2×D13⋊#3862

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

200 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 47 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) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 882);