Finite Group Databasebeta

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C13×#15668735 #50303629

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C7

Aliases

direct productC13×#15668735

Splittings

derived, HallC5×C72 ⋊ C3×C4×C13
HallC13×C7⋊Dic35 ⋊ C3
HallC5×C13×#3862 ⋊ C4
HallC5×C72×C13 ⋊ C3×C4
HallC13×#3862 ⋊ Dic5
HallC7⋊Dic35 ⋊ C3×C13
HallC5×#3862 ⋊ C4×C13
HallC72×C13 ⋊ C3×Dic5
Hall#3862 ⋊ C13×Dic5
HallC5×C13 ⋊ #10596875
SylowC72 ⋊ C3×C13×Dic5
SylowC5 ⋊ C13×#10596875

Subgroups

subgroupG/H
center, hypercenterC2×C13C5⋊#64425
commutator, hypocenterC5×C72C3×C4×C13
FrattiniC2C13×C5⋊#64425
Fitting, socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C13×#3862C2
cosocleC2×C5×C72C2×C3×C13
LCSG ▷ C5×C72
UCSC1 ◁ C2×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 315);