Finite Group Databasebeta

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C2×C3×C72×D65 #50304516

order38220
automorphism?
homologyAbelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C72×D65
unambiguous semidirect product(C2×C5)⋊(C3×C72×D13)

Splittings

Fitting, socleC2×C3×C5×C72×C13 ⋊ C2
derived, HallC5×C13 ⋊ C22×C3×C72
HallC3×C5×C72×C13 ⋊ C22
HallC5×C72×C13 ⋊ C22×C3
HallC3×C72×C13 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D13
HallC72×C13 ⋊ C2×C3×D5
HallC5×C72 ⋊ C2×C3×D13
HallC3×C5×C13 ⋊ C22×C72
HallC3×C13 ⋊ C2×C72×D5
HallC3×C5 ⋊ C2×C72×D13
SylowC13 ⋊ C2×C3×C72×D5
SylowC5 ⋊ C2×C3×C72×D13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72D65
commutator, cosocle, hypocenterC5×C13C22×C3×C72
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C13C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C72

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19110

Conjugacy classes & character table

9996 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1202);