Finite Group Databasebeta

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C5×#21439687 #50303705

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

Aliases

direct productC5×#21439687

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×#14579331 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
Hall#14579331 ⋊ C3×C5
HallC72×C13⋊C3 ⋊ C4×C5
HallC5×C72 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ #5997
HallC5×C13 ⋊ C3×#5997
SylowC72 ⋊ C5×Dic13⋊C3
HallC13⋊C3 ⋊ C5×#5997
SylowC13 ⋊ C3×C5×#5997

Subgroups

subgroupG/H
center, hypercenterC5#21439687
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 391);