Finite Group Databasebeta

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C72×C3⋊#63121 #50304417

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

Aliases

direct productC72×C3⋊#63121
unambiguous semidirect productC3⋊(C72×#63121)

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C72
HallC5×C72×C13 ⋊ Dic3
HallC3×C72×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ #261
HallC72×C13 ⋊ ΓL(1,𝔽16)
HallC5×C72 ⋊ C3⋊#261
HallC3×C72 ⋊ #63121
HallC5×C13 ⋊ C72×Dic3
HallC3×C13 ⋊ C72×AGL(1,𝔽5)
HallC3×C5 ⋊ C72×#261
SylowC13 ⋊ C72×ΓL(1,𝔽16)
SylowC5 ⋊ C72×C3⋊#261
SylowC3 ⋊ C72×#63121

Subgroups

subgroupG/H
center, hypercenterC72C3⋊#63121
commutator, hypocenterC3×C5×C13C4×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C72×D65C2
cosocleC3×D65C2×C72
LCSG ▷ C3×C5×C13
UCSC1 ◁ C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

2646 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1103);