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C3×#27164943 #50304348

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

Aliases

direct productC3×#27164943

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ #261
HallC72×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C72 ⋊ C3×#261
HallC3×C5×C13 ⋊ #5997
HallC3×C72 ⋊ #63122
HallC5×C13 ⋊ C3×#5997
SylowC72 ⋊ C3×#63122
HallC3×C13 ⋊ #11758266
HallC3×C5 ⋊ #14579330
SylowC13 ⋊ C3×#11758266
SylowC5 ⋊ C3×#14579330

Subgroups

subgroupG/H
center, hypercenterC3#27164943
commutator, hypocenterC5×C72×C13C3×C4
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5⋊(C7⋊D91)C2
cosocleC5⋊(C7⋊D91)C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C3

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

2400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1034);