Finite Group Databasebeta

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C5×C13⋊C3×#5997 #50303706

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC5×C13⋊C3×#5997

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C13×#5997 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC13×#5997 ⋊ C3×C5
HallC72×C13⋊C3 ⋊ C4×C5
HallC5×C72 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×#5997
SylowC72 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C5×#5997

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×#5997
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC5×C13⋊C3×C7⋊D7C2
cosocleC13×C7⋊D7C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 392);