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C5×#21439672 #50303707

order38220
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#21439672

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ Dic3
derived, HallC13×#3862 ⋊ C4×C5
HallC5×C13×#3862 ⋊ C4
HallC5×#3862 ⋊ #261
HallC72×C13 ⋊ C5×Dic3
HallC5×C72 ⋊ C3⋊#261
Hall#3862 ⋊ C5×#261
HallC5×C13 ⋊ #10596868
SylowC72 ⋊ C5×C3⋊#261
SylowC13 ⋊ C5×#10596868

Subgroups

subgroupG/H
center, hypercenterC5#21439672
commutator, hypocenterC13×#3862C4×C5
FrattiniC1G
Fitting, socleC5×C72×C13Dic3
prime radicalC5×D13×#3862C2
cosocleD13×#3862C2×C5
LCSG ▷ C13×#3862
UCSC1 ◁ C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 393);