Finite Group Databasebeta

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C5×#21439605 #50303804

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

Aliases

direct productC5×#21439605

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C7⋊(C7⋊#261) ⋊ C3
HallC5×C13×#3862 ⋊ C4
HallC7⋊(C7⋊#261) ⋊ C3×C5
HallC13×#3862 ⋊ C4×C5
HallC5×#3862 ⋊ #261
HallC5×C72 ⋊ C3×#261
Hall#3862 ⋊ C5×#261
HallC5×C13 ⋊ #10596875
SylowC72 ⋊ C3×C5×#261
SylowC13 ⋊ C5×#10596875

Subgroups

subgroupG/H
center, hypercenterC5#21439605
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC5×D13×#3862C2
cosocleC72×D13C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 490);