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C3×C72×#63122 #50304352

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×#63122

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC5×C13 ⋊ C3×C4×C72
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 ⋊ C4×C72
HallC3×C13 ⋊ C72×AGL(1,𝔽5)
HallC3×C5 ⋊ C72×#261
SylowC13 ⋊ C3×C72×AGL(1,𝔽5)
SylowC5 ⋊ C3×C72×#261

Subgroups

subgroupG/H
center, hypercenterC3×C72#63122
commutator, hypocenterC5×C13C3×C4×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C72×D65C2
cosocleD65C2×C3×C72
LCSG ▷ C5×C13
UCSC1 ◁ C3×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1038);