Finite Group Databasebeta

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C72×#63122⋊C3 #50303832

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

Aliases

direct productC72×#63122⋊C3
unambiguous semidirect product#63122⋊(C3×C72)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C72
HallC72×#63122 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC72×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC72×C13 ⋊ C3×AGL(1,𝔽5)
Hall#63122 ⋊ C3×C72
HallC5×C72 ⋊ AGL(1,𝔽13)
HallC5×C13⋊C3 ⋊ C4×C72
HallC13⋊C3 ⋊ C72×AGL(1,𝔽5)
SylowC13 ⋊ C3×C72×AGL(1,𝔽5)
SylowC5 ⋊ C72×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC72#63122⋊C3
commutator, hypocenterC5×C13C3×C4×C72
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC72×C5⋊(D13⋊C3)C2
cosocleD65C2×C3×C72
LCSG ▷ C5×C13
UCSC1 ◁ C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 518);