Finite Group Databasebeta

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C2×C3×C72×D5×C11 #44568937

order32340
automorphism?
homologyAbelianization (H1) = C22×C3×C72×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3×C72×D5×C11
unambiguous semidirect productC5⋊(C22×C3×C72×C11)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C72×C11)

Splittings

Fitting, socleC2×C3×C5×C72×C11 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C72×C11
HallC3×C5×C72×C11 ⋊ C22
HallC5×C72×C11 ⋊ C22×C3
HallC3×C5×C72 ⋊ C22×C11
HallC5×C72 ⋊ C22×C3×C11
HallC3×C5×C11 ⋊ C22×C72
HallC5×C11 ⋊ C22×C3×C72
HallC3×C5 ⋊ C22×C72×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C72×C11D5
commutator, cosocle, hypocenterC5C22×C3×C72×C11
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C72×C11

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16170

Conjugacy classes & character table

12936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 639);